Cycle Attractor Research Articles

Periodic solutions and chaotic attractors of a modified epidemiological SEIS model.

We consider a generalized SEIS (susceptible, exposed, infectious, and susceptible) model where individuals are divided into three compartments: S (healthy and susceptible), E (infected but not just infectious, or exposed), and I (infectious). Finite waiting times in the compartments yield a system of delay-differential or memory equations and may exhibit oscillatory (Hopf) instabilities of the otherwise stationary endemic state, leading normally to regular oscillations in the form of an attractive limit cycle in the phase space spanned by the compartment rates. In the present paper, our aim is to demonstrate that in the dynamics of delayed SEIS models, persistent chaotic attractors can bifurcate from these limit cycles and become accessible if the nonlinear interaction terms fulfill certain basic requirements, which to our knowledge were not addressed in the literature so far. Computing the largest Lyapunov exponent, we show that chaotic behavior exists in a wide parameter range. Finally, we discuss a more general system and show that a sudden falloff of the infection rate with respect to increasing infection number may be responsible for the emergence of chaotic time evolution. Such a falloff can describe mitigation measures, such as wearing masques, individual isolation, or vaccination. The model may have a wide range of interdisciplinary applications beyond epidemic spreading, for instance, in the kinetics of certain chemical reactions.

Anode-Free Zinc-Bromine Batteries Enabled by a Simple Prenucleation Strategy.

The design of anode-free zinc (Zn) batteries with high reversibility at high areal capacity has received significant attention recently, which is quietly challenging yet. Here, a Zn alloyed interface through electroplating is introduced, providing homogeneous Zn prenucleation sites to stabilize subsequent Zn nucleation and plating. By employing Zn-Cu alloy as a module, the complementary simulations and characterizations confirm that the prenucleation alloyed interfaces achieve a homogeneous electric field distribution and greatly enhance the stability of the Zn anode. Accordingly, the Zn//Zn-Cu@Cu half-cells show a long cycle life of over 900h and an average Coulombic efficiency (CE) of 99.8% at an areal capacity of10 mAh cm-2. The assembled anode-free zinc-bromine (Zn-Br2) battery exhibits an attractive stable cycling of 11 000 cycles at 1 mAh cm-2, while over 1000 cycles at the higher areal capacity of 10 mAh cm-2. Excitingly, the Zn-Br2 pouch cell with a capacity of 1000 mAh operates stably over 50 cycles, and achieves successful integration with photovoltaic systems. This anode-free Zn-Br2 batteries constructed through a prenucleation strategy offer new insights into the potential for large-scale energy storage applications.

Attractor-Transition Control of Complex Biological Networks: A Constant Control Approach.

This article presents attractor-transition control of complex biological networks represented by Boolean networks (BNs) wherein the BN is steered from a prescribed initial attractor toward a desired one. The proposed approach leverages the similarity between attractors and Boolean algebraic properties embedded in the underlying state transition equations. To enhance the clarity of expression regarding stabilization toward the desired attractor, a simple coordinate transformation is performed on the considered BN. Based on the characteristics of transformed state equations, self-stabilizing state variables requiring no control efforts are derived in the first. Next, by applying the feedback vertex set (FVS) control scheme, control inputs stabilizing the remaining state variables are determined. The proposed control scheme exhibits versatility by accommodating both fixed-point and cyclic attractors. We validate the effectiveness of the proposed strategy through extensive numerical experiments conducted on random BNs as well as complex biological systems. In adherence to the reproducible research initiative, detailed results of numerical experiments and all the implementation codes are provided on the authors' website: https://github.com/choonlog/AttractorTransition.

Dynamical analysis of bursting in a system with a discontinuous boundary involving two state variables

Abstract This paper investigates the bursting oscillations and the underlying dynamical mechanisms of a non-smooth system with a discontinuous boundary that involves two state variables. A slow-fast non-smooth system is established after modifying the Chua’s circuit. By applying the variable substitution, the system with a boundary involving two state variables is transformed into a system where the boundary involves only a single state variable. The topological equivalence between the systems before and after the transformation is demonstrated. The stability analysis is performed on the transformed system, and the bifurcation conditions are given. Six types of bursting oscillation patterns under different parameter settings are presented. The bifurcation transition mechanisms of these bursting patterns are revealed using two-dimensional transformed phase diagrams. It is found that an increase in the excitation amplitude leads to changes in the transition patterns of the system trajectory between point and cycle, resulting in the formation of a ‘sticking’ special spiking state. This spiking state involves multiple limit cycle attractors and an equilibrium branch. The magnitude of the excitation amplitude also affects the slow passage effect of the system, determining whether the trajectory undergoes periodic oscillations at the Hopf bifurcation point.

Universal dynamical function behind all genetic codes: [formula omitted]-adic attractor dynamical model

The genetic code is a map which gives the correspondence between codons in DNA and amino acids. In the attractor dynamical model (ADM), genetic codes can be described as the sets of the cyclic attractors of discrete dynamical systems - the iterations of functions acting in the ring of 2-adic integers Z2. This ring arises from representation of nucleotides by binary vectors and hence codons by triples of binary vectors. We construct a Universal Function B such that the dynamical functions for all known genetic codes can be obtained from B by simple transformations on the set of codon cycles - the “Addition” and “Division” operations. ADM can be employed for study of phylogenetic dynamics of genetic codes. One can speculate that the “common ancestor genetic code” was caused by B. We remark that this function has 24 cyclic attractors which distribution coincides with the distribution for the hypothetical pre-LUCA code. This coupling of the Universal Function with the pre-LUCA code assigns the genetic codes evolution perspective to ADM. All genetic codes are generated from B through the special chains of the “Addition” and “Division” operations. The challenging problem is to assign the biological meaning to these mathematical operations.

Thirring universe model

In recent years, there has been a significant amount of research focused on Thirring instantons. This study aims to employ the Thirring quantum model as a theoretical Universe model to gain a more profound understanding of the beginning of the Universe. For this, we propose to analyze the entropy of the quantum states of zero energy Thirring instanton solutions and the transition to other quantum states. Our findings by also using Lyapunov exponents and the cyclic attractors as comparative nonlinear methods show that there is no entropy corresponding to instanton solutions with zero energy and that the sudden increase in entropy indicates the formation of the Universe. We evaluate the implications of this study in terms of the standard Universe model. Thus we anticipate that these results have the potential to contribute significantly to our understanding of the origin of the Universe and highlight the role of chaos and complexity in its evolution.

Informed sampling and recommendation of cycling routes: leveraging crowd-sourced trajectories with weighted-latent Dirichlet allocation

Attractive cycling routes can effectively promote active mobility, thus reducing the twin pressures of the population boom and the greenhouse effect. However, the existing approaches for cycling route recommendation primarily concentrate on identifying the most efficient routes while ignoring the urban spatial context, which is essential to meet the user’s particular preferences. This article proposes a novel method for informed sampling and recommending cycling routes leveraging crowd-sourced trajectories with weighted-latent Dirichlet allocation (WLDA). Precisely, spatial context mapping, incorporating a weighting mechanism into LDA, latent topics mining, and cycling route recommendation based on informed sampling are introduced. We collected 1,016 cycling trajectories around Cologne, Germany, for experimental analysis. The experimental results show that the three latent topics within the trajectories, leisure, city, and green tours, are clearly presented in the line density analysis. The insightful recommendation for unfamiliar cyclists could also be actively sampled upon the WLDA model. These findings suggest that our approach could shift the route recommendation paradigm from GIS analysis to a semantic mining perspective, yielding highly interpretable results and offering novel research avenues for applying machine learning in route planning.

Improving Zn2+ migration via designing multiple zincophilic polymer electrolyte for advanced aqueous zinc ion batteries

Aqueous zinc ion batteries (AZIBs)-based on Zn metal anode face serious issues of hydrogen evolution, corrosion, and zinc dendrite growth, limiting their practical applications. Polymer-based electrolytes can effectively inhibit the above issue, but usually bring additional interfacial resistance, resulting in slow reaction kinetics. Herein, we report a poly(4-acryloylmorpholine) electrolyte with multiple zincophilic primitives for fast zinc ion transport at bulk and interface of Zn metal anode (zinc ion transfer number of 0.77) via a facile one-pot polymerization. The special electrolyte structure with multiple zincophilic primitives can adhere tightly to the Zn metal anode and induce uniform Zn deposition, resulting in low interface resistance and enhanced cycling life of batteries. Therefore, the symmetric Zn||Zn batteries assembled based on the designed and synthesized polymer electrolyte can be stably cycled for 1400 with low overpotential (∼220 mV) at 0.5 mA cm−2 with a capacity of 0.5 mAh cm−2, and the corresponding V2O5||Zn full batteries exhibit attractive reversibility, rate performance, and cycling stability. The electrolyte engineering in this work paves a new path for the construction of polymer-based electrolytes for safe and stable AZIBs.

The analysis of tourism development strategies using Tourism Area Life Cycle Theory in Sumberpakem Village, Sumbejambe District

The development of tourism in Sumber Pakem Village has experienced ups and downs. This tourism has been operating since 2019 with the concept of batik educational tourism, but tourist visits are few. In December 2021, the Village Government innovated by establishing a Batik Cultural House, inaugurated as an Eduwisata Village. This effort is only temporary, in 2023 the Batik Cultural House will no longer be operating. This condition threatens the sustainability of Sumber Pakem tourism. This study aims to formulate a strategy for developing Sumber Pakem tourism so that it can survive. Tourism Area Life Cycle (TALC) is the right concept to determine the life cycle of a tourist attraction. This concept can formulate a strategy to revive a tourist attraction, each stage in the TALC model has different characteristics, challenges, and obstacles. Therefore, a different development strategy is needed. This study aims to analyze the position of the life cycle of Sumber Pakem Village appropriately, so that an appropriate and sustainable tourist attraction development strategy can be formulated. The analysis method used is descriptive qualitative. collection of primary and secondary data through interviews and direct observation. The technique for determining informants is purposive sampling. The data analysis technique used triangulation which was then analyzed using TALC and SWOT theories. The results of the study showed that the development of Sumber Pakem Village was in the Involvement cycle, so the strategy that must be implemented is to increase the involvement of pentahelix elements in the tourism planning and development process.

Dynamics of synchronous Boolean networks with non-binary states.

In this paper, we study the dynamics of synchronous Boolean networks and extend previously obtained results for binary Boolean networks to networks with state variables in a general Boolean algebra of 2p elements, with p>1. The method to do this is based on the Stone representation theorem and the relation of such systems on general Boolean algebras with those with binary-state values. Specifically, we deal with the main periodic orbit problems and predecessor problems (existence, coexistence, uniqueness, and number of them), which allows us to determine the periodic structure and the attractor cycles of the system. These results open opportunities to explore novel applications by means of such general systems.

Cellulose fiber-based and engineered capillary foam toward a sustainable, recyclable, and high-performance cushioning structural material

Foam materials have been widely used in cushioning packaging to ensure the integrity of products inside by absorbing energy and preventing collision. However, the extensive use of petroleum-based plastic foams may exacerbate environmental pollution and consume large amounts of energy. Therefore, there has been an increasing focus on producing high-performance and environmentally friendly foams in recent years. In this study, we developed a simple approach for manufacturing cellulose fiber-based capillary foams featuring superior stability and three-dimensional (3D) backbone network cross-linking structure composed of polyvinyl alcohol (PVA) and cationic starch (CS). The resultant capillary foam showed low density (0.154 g/cm3), superior mechanical properties (elastic modulus ranging from 77 to 501 kPa), high energy absorbing efficiency (32.8 %), and low cushioning coefficient (3.0). Besides, the end-of-life cellulose fiber-based capillary foam can be easily recycled for use, showing an attractive closed-loop cycle process. This study presents a unique option for creating affordable, eco-friendly, and malleable foams, demonstrating the potential to substitute the currently used petroleum-based foams in the packaging, food, and transport industries.

Unpredictable tunneling in a retarded bistable potential.

We have studied the rich dynamics of a damped particle inside an external double-well potential under the influence of state-dependent time-delayed feedback. In certain regions of the parameter space, we observe multistability with the existence of two different attractors (limit cycle or strange attractor) with well separated mean Lyapunov energies forming a two-level system. Bifurcation analysis reveals that, as the effects of the time-delay feedback are enhanced, chaotic transitions emerge between the two wells of the double-well potential for the attractor corresponding to the fundamental energy level. By computing the residence time distributions and the scaling laws near the onset of chaotic transitions, we rationalize this apparent tunneling-like effect in terms of the crisis-induced intermittency phenomenon. Further, we investigate the first passage times in this regime and observe the appearance of a Cantor-like fractal set in the initial history space, a characteristic feature of hyperbolic chaotic scattering. The non-integer value of the uncertainty dimension indicates that the residence time inside each well is unpredictable. Finally, we demonstrate the robustness of this tunneling intermittency as a function of the memory parameter by calculating the largest Lyapunov exponent.

Fractional Approach for Belousov-Zhabotinsky Reactions Model with Unified Technique

The Belousov-Zhabotinsky reaction model represents chemical oscillators that exhibit periodic vibrations as a result of complex physic-chemical phenomena. The non-linear behaviour exhibited by Belousov-Zhabotinsky model is the cause of Turing patterns, birth of spiral waves, rise of limit cycle attractors, and deterministic chaos in many chemical reaction processes. Due to these noteworthy characteristics, in this paper, we have analyzed mathematical Belousov-Zhabotinsky model by a novel numerical approach q-Homotopy analysis transformation method. To interpret new observations, we have incorporated Caputo fractional derivative in the model. The numerical result are presented graphically and concerning the absolute error of solutions. With the help of the homotopy parameter curve, we have projected the convergence region with reference to diverse values of fractional derivative. This work establishes that the projected numerical algorithm is a well-organized tool to analyze the multifaceted coupled partial differential equation representing Belousov-Zhabotinsky type reactions.

Layered S-Bridged Covalent Triazine Frameworks via a Bifunctional Template-Catalytic Strategy Enabling High-Performance Zinc-Ion Hybrid Supercapacitors.

Exploring covalent triazine frameworks (CTFs) with high capacitative activity is highly desirable and challenging. Herein, the S-rich CTFs cathode is pioneeringly introduced in Zn-ion hybrid supercapacitors (ZSC), achieving outstanding capacity and energy density, and satisfactory anti-freezing flexibility. Specifically, the S-bridged CTFs are synthesized by a bifunctional template-catalytic strategy, where ZnCl2 serves as both the catalyst/solvent and in situ template to construct triazine frameworks with interconnected pores and layered gaps. The resultant CTFs (CTFS-750) are employed as a reasonable pattern-like system to more deeply scrutinize the synergistic effect of S-bridged triazine and layered porous architecture for polymer-based cathodes in Zn-ion storage. The experimental results indicate that the adsorption barriers of Zn-ions on CTFS-750 are effectively weakened, and accessible Zn2+-absorption sites provided by the C─S─C and C═N bonds have been confirmed via DFT calculations. Consequently, the CTFS-750 cathode-assembled ZSC displays an ultra-high capacity of 211.6 mAh g-1 at 1.0 A g-1, an outstanding energy density of 202.7Wh kg-1, and attractive cycling performance. Moreover, the resulting flexible ZSC device shows superior capacity, good adaptability, and satisfactory anti-freezing behavior. This approach sheds new light on constructing advanced polymer-based cathodes at the atom level and paves the way for fabricating high-performance ZSC and beyond.

Quantifying and Maximizing the Information Flux in Recurrent Neural Networks.

Free-running recurrent neural networks (RNNs), especially probabilistic models, generate an ongoing information flux that can be quantified with the mutual information I[x→(t),x→(t+1)] between subsequent system states x→. Although previous studies have shown that I depends on the statistics of the network's connection weights, it is unclear how to maximize I systematically and how to quantify the flux in large systems where computing the mutual information becomes intractable. Here, we address these questions using Boltzmann machines as model systems. We find that in networks with moderately strong connections, the mutual information I is approximately a monotonic transformation of the root-mean-square averaged Pearson correlations between neuron pairs, a quantity that can be efficiently computed even in large systems. Furthermore, evolutionary maximization of I[x→(t),x→(t+1)] reveals a general design principle for the weight matrices enabling the systematic construction of systems with a high spontaneous information flux. Finally, we simultaneously maximize information flux and the mean period length of cyclic attractors in the state-space of these dynamical networks. Our results are potentially useful for the construction of RNNs that serve as short-time memories or pattern generators.

Efficient bicycle networks and expansion strategies


 
 
 This article explains some of the key attributes and factors relating to efficient bicycle networks and their expansion strategies. Varying from a network scale to brief discussion about the streetscape design, many scientific publications are referenced to explain the crucial aspects which must be taken into consideration when planning an attractive cycling network. Modal switch from other transport modes, especially from cars is one of the goals of this cycling promotion. Various methods such as building new bicycle facilities, improving the quality of existing ones and increasing the comfort and safety of the connections were found to improve the attractiveness of cycling in urban context. Additionally, this article analyses the reasons behind cyclists’ route choice as well as the metrics such as connectedness, directedness and coverage which can be used to measure the level of network functionality. Lastly, network growth under limited resources is considered and an equitable distribution of cycleways across the city is found to be important in preventing neighbourhood segregation while not being too far from a utilitarian kind of distribution in terms of return to investment. 
 
 

Trained recurrent neural networks develop phase-locked limit cycles in a working memory task.

Neural oscillations are ubiquitously observed in many brain areas. One proposed functional role of these oscillations is that they serve as an internal clock, or 'frame of reference'. Information can be encoded by the timing of neural activity relative to the phase of such oscillations. In line with this hypothesis, there have been multiple empirical observations of such phase codes in the brain. Here we ask: What kind of neural dynamics support phase coding of information with neural oscillations? We tackled this question by analyzing recurrent neural networks (RNNs) that were trained on a working memory task. The networks were given access to an external reference oscillation and tasked to produce an oscillation, such that the phase difference between the reference and output oscillation maintains the identity of transient stimuli. We found that networks converged to stable oscillatory dynamics. Reverse engineering these networks revealed that each phase-coded memory corresponds to a separate limit cycle attractor. We characterized how the stability of the attractor dynamics depends on both reference oscillation amplitude and frequency, properties that can be experimentally observed. To understand the connectivity structures that underlie these dynamics, we showed that trained networks can be described as two phase-coupled oscillators. Using this insight, we condensed our trained networks to a reduced model consisting of two functional modules: One that generates an oscillation and one that implements a coupling function between the internal oscillation and external reference. In summary, by reverse engineering the dynamics and connectivity of trained RNNs, we propose a mechanism by which neural networks can harness reference oscillations for working memory. Specifically, we propose that a phase-coding network generates autonomous oscillations which it couples to an external reference oscillation in a multi-stable fashion.

Coexistence of Cyclic Sequential Pattern Recognition and Associative Memory in Neural Networks by Attractor Mechanisms.

Neural networks are developed to model the behavior of the brain. One crucial question in this field pertains to when and how a neural network can memorize a given set of patterns. There are two mechanisms to store information: associative memory and sequential pattern recognition. In the case of associative memory, the neural network operates with dynamical attractors that are point attractors, each corresponding to one of the patterns to be stored within the network. In contrast, sequential pattern recognition involves the network memorizing a set of patterns and subsequently retrieving them in a specific order over time. From a dynamical perspective, this corresponds to the presence of a continuous attractor or a cyclic attractor composed of the sequence of patterns stored within the network in a given order. Evidence suggests that the brain is capable of simultaneously performing both associative memory and sequential pattern recognition. Therefore, these types of attractors coexist within the neural network, signifying that some patterns are stored as point attractors, while others are stored as continuous or cyclic attractors. This article investigates the coexistence of cyclic attractors and continuous or point attractors in certain nonlinear neural networks, enabling the simultaneous emergence of various memory mechanisms. By selectively grouping neurons, conditions are established for the existence of cyclic attractors, continuous attractors, and point attractors, respectively. Furthermore, each attractor is explicitly represented, and a competitive dynamic emerges among these coexisting attractors, primarily regulated by adjustments to external inputs.

A multivariate method of forecasting the nonlinear dynamics of production network based on multilayer neural models

Design of production network based on multilayer neural models is considered in this paper. Design of production network is crucial because it determines the optimal location of production and logistics facilities, affects cost efficiency, customer service level and overall competitiveness in the global market. Multi-layer neural networks play an important role in this process, using advanced algorithms, machine learning models and optimization techniques to analyze huge amounts of data. Special attention is focused on qualitative analysis of dynamic behavior, dynamic lattice model. The model includes rate constants and initial conditions affecting the model trajectories, which can be classified as a stable site, limit cycle, or chaotic attractor. We aim to solve the problem of qualitative behavior of the model as a problem of multilayer neural models. A multivariate method of predicting nonlinear dynamics was used to construct the training data set. Neural networks defined by regenerative architectures with linear and non-linear outputs were analyzed and compared. As a result of the analysis, it was found that architectures with linear outputs show better correspondence between expected and predicted values. Architectures with non-linear outputs, despite their complexity, exhibit less accuracy and more deviation compared to linear ones. The single-layer architecture with linear outputs shows the best accuracy, although the two-layer architecture with linear outputs has the lowest rms error. Architectures with non-linear outputs have faster training times but poor accuracy, while architectures with linear outputs require more training time but have lower errors. The results obtained in the work indicate the importance of choosing the right architecture of the neural network depending on the tasks and requirements for accuracy and training time of the model.

Development of composite separators by coating hydrochloric acid-treated halloysite nanotubes on polypropylene separators for lithium-ion batteries.

In this study, polypropylene/halloysite nanotube (PP/HNT) composite separators were prepared by coating HNTs treated with hydrochloric acid (HCl) of different concentrations on both sides of a PP separator. The effect of HNTs treated with hydrochloric acid (HCl) of different concentrations on the properties of PP/HNT composite separators was investigated. The results indicate that the PP/HNT composite separator exhibits higher electrolyte uptake and wettability than a commercial PP separator, resulting in a better electrochemical performance in Li/LiFePO4 cells. In particular, the PP/HNTs-1.2 M composite separator with HNTs treated with 1.2 M HCl exhibits the highest electrolyte uptake (384%) and ionic conductivity (1.03 mS cm-1). The cells assembled with a PP/HNTs-1.2 M composite separator deliver discharge capacities of 166 mA h g-1 (0.5 C) and 131 mA h g-1 (3 C) with attractive cycling performance (87.6% capacity retention after 100 cycles). HNTs treated with HCl of appropriate concentrations can significantly improve the properties of PP/HNT composite separators for application in lithium-ion batteries.