Attractor States Research Articles

An efficient image encryption scheme using elementary cellular automata with novel permutation box

Digital image communication over public networks requires a high level of security to protect picture elements that represent information. Security is an important and challenging issue that can be solved using cryptography techniques. Generally, image encryption techniques are based on multiple rounds and iterations. In this paper, a secured lightweight cryptosystem is designed based on lookup table operations that reduce computational overhead, resource requirement and power consumption compared to traditional security mechanisms. In this context, one-dimensional elementary cellular automaton has been combined with Henon chaotic map to design a cryptosystem, which can produce unprecedented results in cryptography. Initially, state attractors for rule space are investigated and analyzed in Wolfram’s cellular automata to extract the properties and functional abilities to perform cryptographic operations. A novel algorithm of keyed transposition cipher is applied to digital image in P-Box module to produce shuffled image. Then, the extracted properties of ECA are preserved in a tabular form and further used in the diffusion process. Based on the simulation and comparison with other existing mechanisms, it is evident that the proposed algorithm is promising and obstructive to all kinds of statistical attacks, and it yields security primacy in various areas of cryptography. Encryption/Decryption is based on indexed based lookup tables principal using ECA and can be easily implemented using logic gates. The proposed algorithm provides confidentiality and can be adopted in IoT networks that require lightweight cryptography modules. Experimental results of color and gray images demonstrate flourishing results in the real-time environment of cryptography.

Growing topography due to contrasting rock types in a tectonically dead landscape

Abstract. Many mountain ranges survive in a phase of erosional decay for millions of years following the cessation of tectonic activity. Landscape dynamics in these post-orogenic settings have long puzzled geologists due to the expectation that topographic relief should decline with time. Our understanding of how denudation rates, crustal dynamics, bedrock erodibility, climate, and mantle-driven processes interact to dictate the persistence of relief in the absence of ongoing tectonics is incomplete. Here we explore how lateral variations in rock type, ranging from resistant quartzites to less resistant schists and phyllites, and up to the least resistant gneisses and granitic rocks, have affected rates and patterns of denudation and topographic forms in a humid subtropical, high-relief post-orogenic landscape in Brazil where active tectonics ended hundreds of millions of years ago. We show that catchment-averaged denudation rates are negatively correlated with mean values of topographic relief, channel steepness and modern precipitation rates. Denudation instead correlates with inferred bedrock strength, with resistant rocks denuding more slowly relative to more erodible rock units, and the efficiency of fluvial erosion varies primarily due to these bedrock differences. Variations in erodibility continue to drive contrasts in rates of denudation in a tectonically inactive landscape evolving for hundreds of millions of years, suggesting that equilibrium is not a natural attractor state and that relief continues to grow through time. Over the long timescales of post-orogenic development, exposure at the surface of rock types with differential erodibility can become a dominant control on landscape dynamics by producing spatial variations in geomorphic processes and rates, promoting the survival of relief and determining spatial differences in erosional response timescales long after cessation of mountain building.

Revealing the mechanism of lymphoid and myeloid cell differentiation and transdifferentiation through landscape quantification

The hematopoietic stem cells (HSCs) can differentiate to myeloid and lymphoid lineages, which lead to more specific differentiated cells. This cell fate decision process is governed by an underlying gene regulatory network. However, its underlying mechanism remains to be fully clarified. In this work, based on a gene regulatory network of HSC differentiation, we built a dynamical model and developed an optimization approach to infer model parameters by fitting experimental data quantitatively. We mapped out the potential landscape of HSC differentiation and identified multistable cell states observed in experiments, including multipotent progenitor, B-cell, and macrophage. Interestingly, we also identified one new intermediate cell state on the landscape, which plays a critical role on the cellular transdifferentiation. By calculating the transition action among different attractor states, we quantified kinetic transition paths for differentiation and transdifferentiation between different cell states and identified key genes and regulations during these transition processes. Our work provides a general approach to construct a gene regulatory network model based on experimental data and new insights into the roles of intermediate states on the transdifferentiation process in HSC development.2 MoreReceived 22 September 2020Accepted 9 February 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013186Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasComplex systemsPhysical SystemsGene regulatory networksNonequilibrium systemsInterdisciplinary PhysicsNetworksBiological Physics

A global and physical mechanism of gastric cancer formation and progression

Gastric cancer is regarded as a major health issue for human being nowadays. The Helicobacter pylori (H. pylori) infection has been found to accelerate the development of gastritis and gastric cancer. Significant efforts have been made towards the understanding of the biology of gastric cancer on both genetic and epigenetic levels. However the physical mechanism behind the gastric cancer formation is still elusive. In this study, we constructed a model for investigating gastric cancer formation by explored the gastric cancer landscape and the flow flux. We uncovered three stable state attractors on the landscape: normal, gastritis and gastric cancer. The definition of each attractor is based on the biological function and gene expression levels. The global stabilities and the switching processes were quantified through the barrier heights and dominant kinetic paths. To investigate the underlying mechanism of the process from normal through the gastritis to the gastric cancer caused by genetic or epigenetic factors, we simulate the oncogenesis of gastric cancer through changes of several gene regulation strengths and H. pylori infection. The simulated results can illustrate the developmental and metastasis process of gastric cancer. Different H. pylori infection degrees accelerating the process from gastritis to gastric cancer can be quantified. Then we applied global sensitivity analysis, one key gene and four key regulations were found. These results are consist with the experimental results and can be used to design the polygenic anti-cancer agents through multiple key genes or regulations. The landscape approach provides a physical and simple strategy for analyzing gastric cancer in a systematic and quantitative way. It also offers new insight into treatment strategy for gastric cancer by adjusting relevant polygenic genes and regulations.

The complex dynamics of adaptive teaching: observing teacher-student interaction in the language classroom

Abstract Real-time verbal interactions between foreign language teachers and their students are of vital importance for language development, but classroom interactions are also multi-faceted and complex. The way a teacher understands and responds to learner utterances can be a powerful pedagogical strategy to scaffold learner language development. In this paper we present the Questions and Answers in English Language Teaching coding scheme which can be used to observe and describe the dynamics of teacher questions and student responses in language classrooms. We piloted the instrument in English as a foreign language lessons of four experienced teachers teaching 16 lessons in total. State Space Grids were used to visualize classroom dynamics and quantify intra-individual variability of each lesson. The results show that interactions between teachers and students have the tendency to self-organize and stabilize in one specific area of the grid. Lessons taught by three of the teachers revealed a dominant pattern formed by closed questions and short student responses. One teacher taught lessons in which more complex question and answer sequences were prevalent. These patterns of variability and stability show that teacher-student interactions have the properties of a shallow attractor state. The analysis of moment-to-moment turns in classroom interaction indicate that students in this study generally adapt their response to the level of teacher questions, but that teachers do not seem to adapt their questions to the level of the previous student answer. This suggests that, even for experienced teachers, scaffolding and adaptive teaching might be easier said than done.

Coordinated Prefrontal State Transition Leads Extinction of Reward-Seeking Behaviors

Extinction learning suppresses conditioned reward responses and is thus fundamental to adapt to changing environmental demands and to control excessive reward seeking. The medial prefrontal cortex (mPFC) monitors and controls conditioned reward responses. Abrupt transitions in mPFC activity anticipate changes in conditioned responses to altered contingencies. It remains, however, unknown whether such transitions are driven by the extinction of old behavioral strategies or by the acquisition of new competing ones. Using in vivo multiple single-unit recordings of mPFC in male rats, we studied the relationship between single-unit and population dynamics during extinction learning, using alcohol as a positive reinforcer in an operant conditioning paradigm. To examine the fine temporal relation between neural activity and behavior, we developed a novel behavioral model that allowed us to identify the number, onset, and duration of extinction-learning episodes in the behavior of each animal. We found that single-unit responses to conditioned stimuli changed even under stable experimental conditions and behavior. However, when behavioral responses to task contingencies had to be updated, unit-specific modulations became coordinated across the whole population, pushing the network into a new stable attractor state. Thus, extinction learning is not associated with suppressed mPFC responses to conditioned stimuli, but is anticipated by single-unit coordination into population-wide transitions of the internal state of the animal.SIGNIFICANCE STATEMENT The ability to suppress conditioned behaviors when no longer beneficial is fundamental for the survival of any organism. While pharmacological and optogenetic interventions have shown a critical involvement of the mPFC in the suppression of conditioned responses, the neural dynamics underlying such a process are still largely unknown. Combining novel analysis tools to describe behavior, single-neuron response, and population activity, we found that widespread changes in neuronal firing temporally coordinate across the whole mPFC population in anticipation of behavioral extinction. This coordination leads to a global transition in the internal state of the network, driving extinction of conditioned behavior.

Student perceptions of a mobile learning application for English Oral Presentations: the case of EOPA

This study investigated student perceptions and opinions on an English Oral Presentation Application (EOPA), a mobile learning application designed to assist English learners develop oral presentations and online collaboration skills. This study was part of a Design Based Research (DBR) project which incorporated an adapted Technology Acceptance Model (TAM) questionnaire to gain insights on students’ perceptions towards EOPA. In addition, focus-group interviews were used to discover the external and internal factors involved in this type of mobile learning. Participants were 30 Taiwanese undergraduate students who took part in a six-week training course. The questionnaire results indicated that 37% of students found EOPA to be useful for learning, but 33% also found it inconvenient to use. Furthermore, attitudes towards learning suggested they had some difficulties using the app. To gain a deeper understanding of why students use EOPA and to discover other app-related learning problems, the interviews were explored using a Complex Dynamic Systems approach to find the attractor and repeller dynamic states in the learning system. These included the language and presentation skills, the multimedia learning material, app design, online collaboration, anxiety, and limited self-regulation skills. The findings will be used to refine EOPA and the oral presentation learning framework. The study demonstrates how the discovery of different dynamic states can be used to improve mobile learning design.

Basal Ganglia and Thalamic Contributions to Language Function: Insights from A Parallel Distributed Processing Perspective.

Cerebral representations are encoded as patterns of activity involving billions of neurons. Parallel distributed processing (PDP) across these neuronal populations provides the basis for a number of emergent properties: 1) processing occurs and knowledge (long term memories) is stored (as synaptic connection strengths) in exactly the same networks; 2) networks have the capacity for setting into stable attractor states corresponding to concepts, symbols, implicit rules, or data transformations; 3) networks provide the scaffold for the acquisition of knowledge but knowledge is acquired through experience; 4) PDP networks are adept at incorporating the statistical regularities of experience as well as frequency and age of acquisition effects; 5) networks enable content-addressable memory; 6) because knowledge is distributed throughout networks, they exhibit the property of graceful degradation; 7) networks intrinsically provide the capacity for inference. This paper details the features of the basal ganglia and thalamic systems (recurrent and distributed connectivity) that support PDP. The PDP lens and an understanding of the attractor trench dynamics of the basal ganglia provide a natural explanation for the peculiar dysfunctions of Parkinson's disease and the mechanisms by which dopamine deficiency is causal. The PDP lens, coupled with the fact that the basal ganglia of humans bears strong homology to the basal ganglia of lampreys and the central complex of arthropods, reveals that the fundamental function of the basal ganglia is computational and involves the reduction of the vast dimensionality of a complex multi-dimensional array of sensorimotor input into the optimal choice from a small repertoire of behavioral options - the essence of reactive intention (automatic responses to sensory input). There is strong evidence that the sensorimotor basal ganglia make no contributions to cognitive or motor function in humans but can cause serious dysfunction when pathological. It appears that humans, through the course of evolution, have developed cortical capacities (working memory and volitional and reactive attention) for managing sensory input, however complex, that obviate the need for the basal ganglia. The functions of the dorsal tier thalamus, however, even viewed with an understanding of the properties of population encoded representations, remain somewhat more obscure. Possibilities include the enabling of attractor state constellations that optimize function by taking advantage of simultaneous input from multiple cortical areas; selective engagement of cortical representations; and support of the gamma frequency synchrony that enables binding of the multiple network representations that comprise a full concept representation.

Quantifying the Stability of Coupled Genetic and Epigenetic Switches With Variational Methods.

The Waddington landscape provides an intuitive metaphor to view development as a ball rolling down the hill, with distinct phenotypes as basins and differentiation pathways as valleys. Since, at a molecular level, cell differentiation arises from interactions among the genes, a mathematical definition for the Waddington landscape can, in principle, be obtained by studying the gene regulatory networks. For eukaryotes, gene regulation is inextricably and intimately linked to histone modifications. However, the impact of such modifications on both landscape topography and stability of attractor states is not fully understood. In this work, we introduced a minimal kinetic model for gene regulation that combines the impact of both histone modifications and transcription factors. We further developed an approximation scheme based on variational principles to solve the corresponding master equation in a second quantized framework. By analyzing the steady-state solutions at various parameter regimes, we found that histone modification kinetics can significantly alter the behavior of a genetic network, resulting in qualitative changes in gene expression profiles. The emerging epigenetic landscape captures the delicate interplay between transcription factors and histone modifications in driving cell-fate decisions.

A Study of Students’ Motivational Dynamics in College English Classes

Students’ motivation in learning English in class is not static but dynamic and multidimensional. This has been recognized by more and more researchers, but studies of this phenomenon are still in early stage. Besides, researches on Macau local university students’ (non-English majors) learning motivation in English class on the basis of Dynamic Systems Theory have not been found. In order to explore the features of these students’ learning motivation in English class, and find out the factors that influence their English learning, a case study is conducted to investigate the change of students’ motivation in learning English in the classroom context. It reveals that under the influence of different situational contexts and external factors, the change of students’ motivation in learning English shows individual differences, while at the same time follows some certain patterns - the attractor state. These findings may be beneficial to English teaching and learning in Macau universities, helping teachers better motivate Macau local students to learn English in class.

КОНТРОЛЬНІ КАРТИ ШУХАРТА В ЗАДАЧАХ ДІАГНОСТИКИ СТАЛОГО РОЗВИТКУ ТЕРИТОРІЇ

Inconsistency and instability of planning processes are some of the important obstacles to achieving the goals of sustainable development of Ukraine today. This indicates the imperfection of the analytical function of the management system of sustainable development of the territory, which is associated with the forecasting and diagnosis of development processes. The thresholds of indicators for diagnosing the state of the territory by the level of stability (homeostasis) are fundamental, i.e. acceptable limit values, non-compliance (exceeding or not reaching) which leads to the emergence of destructive processes in the territory. The legislative approach is used in domestic practice to determine the threshold values of indicators, based on expert assessments of specialists. But the expert definition of these indicators is sufficiently subjective, which, in turn, does not preclude fundamental errors in diagnosing the state of the territory. In order to prevent subjectivism, it is advisable to use Shewhart control charts as a diagnostic tool to identify the uncontrolled state of the territory and answer the question: should or should not interfere with the system? The theory of control charts largely corresponds to the main provisions of the theories of sustainable development and «The Black Swan». Development is considered as a sequence of long periods in the theory of sustainable development, which is based on the basic principles of synergetic and nonlinear dynamics. These periods correspond to the stable states of the system (homeostasis), which are interrupted by periods of bifurcation (chaos). After a period of chaos, the system moves to the next qualitatively new steady state (attractor), the choice of which is usually determined by fluctuations (i.e., difficult to predict, new events, the so-called «Black Swans») at the bifurcation point. To study the problems of controllability of the process of sustainable development of the territory, the most suitable are Shewhart’s individuals control chart (X) and moving range (mR), which are used for periodic monitoring data and rapid detection of special causes (fluctuations). On the example of interpreting the results of XmR chart to diagnose the manageability of human development in Ukraine and Kuwait for 1990-2019 proved the feasibility of using a combined XmR chart in diagnosing the state of the territory on indicators or integrated indices that characterize various aspects of development.

Understanding the Continuous-Time Dynamics of Phase-Transition Nano-Oscillator-Based Ising Hamiltonian Solver

Many combinatorial optimization problems can be mapped onto the ground-state search problem of an Ising model. Exploiting the continuous-time dynamics of a network of coupled phase-transition nano-oscillators (PTNOs) allows building an Ising Hamiltonian solver for obtaining optimum or near-optimum solution with a large speed-up over discrete-time iterative digital hardware. Here, we provide insights into the continuous-time dynamics of such a PTNO-based Ising Hamiltonian solver. We highlight the formation of stable attractor states in the phase space of the coupled PTNO network using second-harmonic injection locking (SHIL) that corresponds to the minima of the Ising Hamiltonian. We show that the emergent synchronized dynamics of the PTNO network is maximized near the critical point of oscillator phase bistability beyond which the dynamics is limited by freeze-out effects. Such dynamical freeze-out severely limits the performance of the PTNO-based Ising solver from obtaining the global optimum. We highlight an improvement in the success probability of reaching the ground state by introducing an annealing scheme with linearly increasing SHIL amplitude compared with a constant SHIL. Finally, we estimate the “effective temperature” of the PTNO-based Ising solver by comparing it with the Markov chain Monte Carlo simulations. The PTNO-based Ising solver behaves like a low-temperature Ising spin system, indicating its effectiveness for optimization tasks.

Understanding visual attention with RAGNAROC: A reflexive attention gradient through neural AttRactOr competition.

A quintessential challenge for any perceptual system is the need to focus on task-relevant information without being blindsided by unexpected, yet important information. The human visual system incorporates several solutions to this challenge, 1 of which is a reflexive covert attention system that is rapidly responsive to both the physical salience and the task-relevance of new information. This article presents a model that simulates behavioral and neural correlates of reflexive attention as the product of brief neural attractor states that are formed across the visual hierarchy when attention is engaged. Such attractors emerge from an attentional gradient distributed over a population of topographically organized neurons and serve to focus processing at 1 or more locations in the visual field, while inhibiting the processing of lower priority information. The model moves toward a resolution of key debates about the nature of reflexive attention, such as whether it is parallel or serial, and whether suppression effects are distributed in a spatial surround, or selectively at the location of distractors. The model also develops a framework for understanding the neural mechanisms of visual attention as a spatiotopic decision process within a hierarchy and links them to observable correlates such as accuracy, reaction time (RT), and the N2pc and PD components of the electroencephalogram (EEG). This last contribution is the most crucial for repairing the disconnect that exists between our understanding of behavioral and neural correlates of attention. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Bifurcations and the Emergence of L2 Syntactic Structures in a Complex Dynamic System.

We report on a complex dynamic systems study of an untutored adult French learner’s development of English syntax, specifically two non-finite adverbial constructions. The study was conducted over one academic year of 30 weeks. From an analysis of L2 speech samples collected weekly, certain patterns in the flux emerged. The learner’s ensuing second language development is characterized by a series of bifurcations, stemming from forms competing for the same functional terrain. Each bifurcation is accompanied by turbulence as the system moves from one attractor state to another. The transition is characterized by loss of stability, an increase in variability, and a period of dysfluency. It is in the dynamic relationship of accuracy and fluency that novel syntactic forms emerge, both convergent with and divergent from dominant contextual patterns, with dominance established by consulting a well-known corpus of contemporary English. Non-linear development occurs with continuous and iterative exposure to and interaction in English—from relexification to adaptation and synchronization, animated by the learner’s perception and memory of regular sequential associations, to pruning of divergent forms. What results over time is a branching hierarchy, connecting online processing with over time development. Multiple competing forms continue to co-exist in the learner’s repertoire, which is likely more typical of adult L2 development than of L1 acquisition.

Modelling the impact of structural directionality on connectome-based models of neural activity

AbstractUnderstanding structure--function relationships in the brain remains an important challenge in neuroscience. However, whilst structural brain networks are intrinsically directed, due to the prevalence of chemical synapses in the cortex, most studies in network neuroscience represent the brain as an undirected network. Here, we explore the role that directionality plays in shaping transition dynamics of functional brain states. Using a system of Hopfield neural elements with heterogeneous structural connectivity given by different species and parcellations (cat, Caenorhabditis elegans and two macaque networks), we investigate the effect of removing directionality of connections on brain capacity, which we quantify via its ability to store attractor states. In addition to determining large numbers of fixed-point attractor sets, we deploy the recently developed basin stability technique in order to assess the global stability of such brain states, which can be considered a proxy for network state robustness. Our study indicates that not only can directed network topology have a significant effect on the information capacity of connectome-based networks, but it can also impact significantly the domains of attraction of the aforementioned brain states. In particular, we find network modularity to be a key mechanism underlying the formation of neural activity patterns, and moreover, our results suggest that neglecting network directionality has the scope to eliminate states that correlate highly with the directed modular structure of the brain. A numerical analysis of the distribution of attractor states identified a small set of prototypical direction-dependent activity patterns that potentially constitute a `skeleton' of the non-stationary dynamics typically observed in the brain. This study thereby emphasizes the substantial role network directionality can have in shaping the brain's ability to both store and process information.

Recurrent amplification of grid-cell activity.

High-level cognitive abilities such as navigation and spatial memory are thought to rely on the activity of grid cells in the medial entorhinal cortex (MEC), which encode the animal's position in space with periodic triangular patterns. Yet the neural mechanisms that underlie grid-cell activity are still unknown. Recent in vitro and in vivo experiments indicate that grid cells are embedded in highly structured recurrent networks. But how could recurrent connectivity become structured during development? And what is the functional role of these connections? With mathematical modeling and simulations, we show that recurrent circuits in the MEC could emerge under the supervision of weakly grid-tuned feedforward inputs. We demonstrate that a learned excitatory connectivity could amplify grid patterns when the feedforward sensory inputs are available and sustain attractor states when the sensory cues are lost. Finally, we propose a Fourier-based measure to quantify the spatial periodicity of grid patterns: the grid-tuning index.

Transition to coarse-grained order in coupled logistic maps: Effect of delay and asymmetry

• We study transition to two band attractor state in coupled logistic maps with linear/nonlinear coupling and delay. • For nonlinear coupling with even delay/ linear coupling with odd delay, we find antiferromagnetic order at critical point. • For linear coupling with even delay/ nonlinear coupling with odd delay, we observe ferromagnetic order at critical point. • The persistence exponent for antiferromagnetic ordering is 0.375. For ferromagnetic ordering it is 0.285. We study one-dimensional coupled logistic maps with delayed linear or nonlinear nearest-neighbor coupling. Taking the nonzero fixed point of the map x * as reference, we coarse-grain the system by identifying values above x * with the spin-up state and values below x * with the spin-down state. We define persistent sites at time T as the sites which did not change their spin state even once for all even times till time T . A clear transition from asymptotic zero persistence to non-zero persistence is seen in the parameter space. The transition is accompanied by the emergence of antiferromagnetic, or ferromagnetic order in space. We observe antiferromagnetic order for nonlinear coupling and even delay, or linear coupling and odd delay. We observe ferromagnetic order for linear coupling and even delay, or nonlinear coupling and odd delay. For symmetric coupling, we observe a power-law decay of persistence. The persistence exponent is close to 0.375 for the transition to antiferromagnetic order and close to 0.285 for ferromagnetic order. The number of domain walls decays with an exponent close to 0.5 in all cases as expected. The persistence decays as a stretched exponential and not a power-law at the critical point, in the presence of asymmetry.

Attractor-state itinerancy in neural circuits with synaptic depression

Neural populations with strong excitatory recurrent connections can support bistable states in their mean firing rates. Multiple fixed points in a network of such bistable units can be used to model memory retrieval and pattern separation. The stability of fixed points may change on a slower timescale than that of the dynamics due to short-term synaptic depression, leading to transitions between quasi-stable point attractor states in a sequence that depends on the history of stimuli. To better understand these behaviors, we study a minimal model, which characterizes multiple fixed points and transitions between them in response to stimuli with diverse time- and amplitude-dependencies. The interplay between the fast dynamics of firing rate and synaptic responses and the slower timescale of synaptic depression makes the neural activity sensitive to the amplitude and duration of square-pulse stimuli in a nontrivial, history-dependent manner. Weak cross-couplings further deform the basins of attraction for different fixed points into intricate shapes. We find that while short-term synaptic depression can reduce the total number of stable fixed points in a network, it tends to strongly increase the number of fixed points visited upon repetitions of fixed stimuli. Our analysis provides a natural explanation for the system’s rich responses to stimuli of different durations and amplitudes while demonstrating the encoding capability of bistable neural populations for dynamical features of incoming stimuli.

Chaotic motion of time-delay fractional order financial dynamic system of single sliding mode control

In this paper, the equations of time-delay fractional order financial dynamic system are studied. Firstly, the dynamic characteristics of the time-delay fractional order financial system with are analyzed. Secondly, the attractor state change of the time-delay fractional order financial system induced by disturbance is studied. By adding specific uncertainties and disturbances to the specified state variables of the system, the attractor of the system is induced to change. Finally, the classical integral sliding mode control method is used to design a single controller to control the time-delay fractional order financial system from chaos to fixed point, and the feasibility and robustness of the control scheme have been proved theoretically and verified by the simulation.

Buildup and bistability in auditory streaming as an evidence accumulation process with saturation.

A repeating triplet-sequence ABA− of non-overlapping brief tones, A and B, is a valued paradigm for studying auditory stream formation and the cocktail party problem. The stimulus is “heard” either as a galloping pattern (integration) or as two interleaved streams (segregation); the initial percept is typically integration then followed by spontaneous alternations between segregation and integration, each being dominant for a few seconds. The probability of segregation grows over seconds, from near-zero to a steady value, defining the buildup function, BUF. Its stationary level increases with the difference in tone frequencies, DF, and the BUF rises faster. Percept durations have DF-dependent means and are gamma-like distributed. Behavioral and computational studies usually characterize triplet streaming either during alternations or during buildup. Here, our experimental design and modeling encompass both. We propose a pseudo-neuromechanistic model that incorporates spiking activity in primary auditory cortex, A1, as input and resolves perception along two network-layers downstream of A1. Our model is straightforward and intuitive. It describes the noisy accumulation of evidence against the current percept which generates switches when reaching a threshold. Accumulation can saturate either above or below threshold; if below, the switching dynamics resemble noise-induced transitions from an attractor state. Our model accounts quantitatively for three key features of data: the BUFs, mean durations, and normalized dominance duration distributions, at various DF values. It describes perceptual alternations without competition per se, and underscores that treating triplets in the sequence independently and averaging across trials, as implemented in earlier widely cited studies, is inadequate.