Dynamical Systems Approach Research Articles

Dynamics of Poisson-Boltzmann equations: “Hidden” mechanisms for Gouy-Chapman layer and beyond

In this work a dynamical system approach is taken to systematically investigate the one-dimensional classical Poisson-Boltzmann (PB) equation with various boundary conditions. This framework has a unique advantage of a geometric view of the dynamical systems, which allows one to reveal and examine critical features of the PB models. More specifically, we are able to reveal the mechanism of Gouy-Chapman layer: the presence of an equilibrium for the PB equation, including equilibrium-at-infinity for Gouy-Chapman's original setup as the limiting case. Several other critical, somehow counterintuitive, features revealed in this work are the saturation phenomenon of surface charge density, the uniform boundedness of electric pressure (given length) and of length (given electric pressure) in surface charge, and the critical length for a reversal of electric force direction. All have a common mechanism: the presence of an equilibrium for the PB equation. We believe that the critical features presented from the classical PB models persist for modified PB systems up to a certain degree.By all means, these findings are by chance which is probably why the mechanism has been missing after the phenomenon of Gouy-Chapmann layer and alike had been discovered for very long. Only when viewed from the nonlinear dynamical systems theory, these results become rather apparent.

Amplitude death in ring-coupled network with asymmetric thermoacoustic oscillators and nonlocal time-delay interactions

AbstractThis numerical study examines the pressure amplitude distribution, focusing on amplitude death, in a ring-coupled network of nonlocally coupled asymmetric thermoacoustic oscillators. Each decoupled self-excited thermoacoustic oscillator is modeled using the classical Rijke tube model. We investigate three configurations with asymmetric thermoacoustic oscillators: localized asymmetry, side-by-side asymmetry, and alternating asymmetry. Asymmetries are introduced through frequency detuning and heater power mismatching. Our study reveals that the configuration with alternating asymmetry induces the largest region of amplitude death compared to the other two configurations, where all originally self-excited oscillators become quenched in the network. The remaining energy of oscillations often concentrates at the two ends of the axis of symmetry. The region of amplitude death generally increases with the number of thermoacoustic oscillators and remains unchanged when the number of oscillators is sufficiently large (n = 8). The variation of the global average pressure amplitude predicted by the proposed model qualitatively agrees with previous experimental observations. In summary, we conclude: (1) reduced-order models developed from a dynamical system approach can provide a qualitative prediction of the system’s pressure amplitude distribution, potentially offering useful information for avoiding operating parameters that lead to high-amplitude thermoacoustic oscillations in multi-combustor systems; and (2) introducing asymmetries into a ring-coupled network can potentially be leveraged to weaken self-excited oscillations in multi-combustor systems globally.

Natural convection in a vertical channel. Part 2. Oblique solutions and global bifurcations in a spanwise-extended domain

Vertical thermal convection is a non-equilibrium system in which both buoyancy and shear forces play a role in driving the convective flow. Beyond the onset of convection, the driven dissipative system exhibits chaotic dynamics and turbulence. In a three-dimensional domain extended in both the vertical and the transverse dimensions, Gao et al. (Phys. Rev. E, vol. 97, 2018, 053107) have observed a variety of convection patterns which are not described by linear stability analysis. We investigate the fully nonlinear dynamics of vertical convection using a dynamical-systems approach based on the Oberbeck–Boussinesq equations. We compute the invariant solutions of these equations and the bifurcations that are responsible for the creation and termination of various branches. We map out a sequence of local bifurcations from the laminar base state, including simultaneous bifurcations involving patterned steady states with different symmetries. This atypical phenomenon of multiple branches simultaneously bifurcating from a single parent branch is explained by the role of $D_4$ symmetry. In addition, two global bifurcations are identified: first, a homoclinic cycle from modulated transverse rolls and second, a heteroclinic cycle linking two symmetry-related diamond-roll patterns. These are confirmed by phase space projections as well as the functional form of the divergence of the period close to the bifurcation points. The heteroclinic orbit is shown to be robust and to result from a 1:2 mode interaction. The intricacy of this bifurcation diagram highlights the essential role played by dynamical systems theory and computation in hydrodynamic configurations.

Dynamical system approach of interacting dark energy models in $f(R,T^{\phi})$ gravity

Abstract We have examined an isotropic and homogeneous cosmological model in $f(R,T^{\phi})$ gravity, where $R$ represents the Ricci scalar and $T^{\phi}$ exhibits the energy momentum tensor's trace. We examine the stability criteria by performing the dynamical system analysis for our model $f(R,T^{\phi})=R+2(aT^{\phi}+b)$, where $a$ $\&$ $b$ are the constants. We derive a set of autonomous equations and find their solutions by assuming a flat potential $V_{0}$. We assess the equilibrium points from these equations and find the eigenvalues. We analyze the physical interpretation of the phase space for this system. We obtain three stable equilibrium points. We also examine the interaction between scalar field and dark energy, represented by $Q=\psi H\rho_{de}$ and determine the equilibrium points for this interaction. We identify four stable equilibrium points for this interaction. We calculate the values of the physical parameters for both scenarios at each equilibrium point, indicating the Universe's accelerated expansion.

A dynamical systems approach to optimal foraging

Foraging for resources in an environment is a fundamental activity that must be addressed by any biological agent. Modelling this phenomenon in simulations can enhance our understanding of the characteristics of natural intelligence. In this work, we present a novel approach to model foraging in-silico using a continuous coupled dynamical system. The dynamical system is composed of three differential equations, representing the position of the agent, the agent’s control policy, and the environmental resource dynamics. Crucially, the control policy is implemented as a parameterized differential equation which allows the control policy to adapt in order to solve the foraging task. Using this setup, we show that when these dynamics are coupled and the controller parameters are optimized to maximize the rate of reward collected, adaptive foraging emerges in the agent. We further show that the internal dynamics of the controller, as a surrogate brain model, closely resemble the dynamics of the evidence accumulation mechanism, which may be used by certain neurons of the dorsal anterior cingulate cortex region in non-human primates, for deciding when to migrate from one patch to another. We show that by modulating the resource growth rates of the environment, the emergent behaviour of the artificial agent agrees with the predictions of the optimal foraging theory. Finally, we demonstrate how the framework can be extended to stochastic and multi-agent settings.

A New High-Order Fractional Parallel Iterative Scheme for Solving Nonlinear Equations

Solving fractional-order nonlinear equations is crucial in engineering, where precision and accuracy are essential. This study introduces a novel fractional parallel technique for solving nonlinear equations. To enhance convergence, we incorporate a simple root-finding method of order 3γ + 1 as a correction term in the parallel scheme. Theoretical analysis shows that the parallel scheme achieves a convergence order of 6γ + 3. Using a dynamical system approach, we identify optimal parameter values, and the symmetry in the dynamical planes for different fractional parameters demonstrates the method’s stability and consistency in handling nonlinear problems. These parameter values are applied to the parallel scheme, yielding highly consistent results. Several engineering problems are examined to assess the method’s efficiency, stability, and consistency compared to existing methods.

Constructing viable interacting dark matter and dark energy models: a dynamical systems approach

We study the evolution of k = -1 FLRW cosmological models for two interacting Dark Matter-Dark Energy Models using dynamical system analysis. Since we are interested in late time evolution, the sign of the interaction term is chosen such that it facilitates the transfer of energy from dark matter to dark energy. We also explore the k = 0 invariant subspace of these models. We find that both these models have sectors which have a stable fixed point where we can recover an accelerating universe with a negative equation of state. This indicates these can be viable models for our universe. We also rule out certain sectors of these models because they do not give the correct late time observational features. We observe that although we start with a dust-like Dark Matter, its effective equation of state evolves due to its interaction with Dark Energy. As a result, the Dark Matter can display features of stiff matter and exotic matter in the course of evolution.

A Network Control Theory of Dynamic Systems Approach to Personalize Therapy

Contemporary latent disease models of psychopathology have shown limited clinical utility and the efficacy of conventional treatments have been disappointing. An alternative approach offers the network approach and a dynamic systems perspective to psychopathology and treatment change. To understand and modify dynamic systems, engineering and mathematics have been relying on principles of network control theory. This article will discuss the application of network control theory of dynamic systems approach to personalize therapy. Network control theory can be used as a guide for personalizing treatment by choosing the most promising intervention strategy targeting the change processes based on the network structure. A composit case illustration will demonstrate the principles and application of network control theory to therapy in practice within the framework of process-based therapy. In conclusion, a network control theory of dynamic systems approach is highly relevant and applicable to clinical science.

Time-periodic traveling waves and propagating terraces for multistable equations with a fractional Laplacian: An abstract dynamical systems approach

This paper is devoted to studying the existence of traveling wave solutions for reaction-diffusion equations with fractional Laplacians in time-periodic environments. By developing a dynamical systems approach, we establish the existence of propagating terraces for equations with multistable nonlinearities, which consequently implies the existence of bistable traveling waves. Furthermore, we investigate whether traveling waves exist in the multistable case. We provide an affirmative answer to this question for a special type of nonlinearity in high-frequency oscillating environments, and determine the homogenized limit of the traveling waves as the period approaches 0.

Characterization of Electric Field Fluctuations in the High-Latitude Ionosphere Using a Dynamical Systems Approach: CSES-01 Observations

We present an analysis of the ionospheric electric field dynamics at high latitudes during periods of quiet and disturbed geomagnetic activity by exploiting recent advancements in dynamical systems and extreme value theory. Specifically, we employed two key indicators: the instantaneous dimension d, which evaluates the degrees of freedom within the system, and the extremal index θ, which quantifies the system’s persistence in a given state. Electric field measurements were obtained from the CSES-01 satellite at mid- and high latitudes in the Southern Hemisphere. Our analysis revealed that the instantaneous dimension increases upon crossing specific ionospheric regions corresponding to the auroral oval boundaries. Outside these regions, the instantaneous dimension fluctuates around the state-space dimension, suggesting an ergodic nature of the system. As geomagnetic activity intensifies, differences in the properties of various ionospheric regions persist, albeit with an increased system instability characterized by higher θ values, thus indicating the externally driven nature of the electric field response to geomagnetic activity. This study provides new insights into the spatial and temporal variability of electric field fluctuations in the ionosphere, highlighting the complex interplay between geomagnetic conditions and ionospheric dynamics.

Modeling of Energy Usage Intensity Based on West Java Region Conditions Using Dynamic Systems Approach

Abstract West Java is a region in Indonesia experiencing significant population growth and economic activity, leading to a substantial increase in energy demand and presenting challenges for sustainable energy resource management. Energy is fundamental to economic and social activities, and efficient, sustainable management is essential for balancing economic growth with environmental preservation. Modeling energy usage intensity is crucial for understanding the dynamics of energy consumption and its influencing factors. This study aims to develop a model that accurately represents energy consumption patterns in West Java using a dynamic systems approach. The study utilizes Causal Loop Diagrams (CLD) and Stock Flow Diagrams (SFD) to systematically map and model the intricate dynamics of the energy system, providing a comprehensive understanding of the interactions and influences among various factors. The model was validated by comparing its outputs with historical data and calculating a Mean Absolute Percentage Error (MAPE). This enhances confidence in the analyses and recommendations derived from the model, making it a valuable tool for understanding and influencing energy usage patterns in West Java. In conclusion, this study not only provides deep insights into energy consumption in West Java but also offers practical approaches for improved energy management, supporting sustainable development and environmental protection in the region.

The infant parasympathetic nervous system is socially embedded and dynamic at multiple timescales, within and between people.

Human interpersonal capacities emerge from coordinated neural, biological, and behavioral activity unfolding within and between people. However, developmental research to date has allocated comparatively little focus to the dynamic processes of how social interactions emerge across these levels of analysis. Second-person neuroscience and dynamic systems approach together to offer an integrative framework for addressing these questions. This study quantified respiratory sinus arrhythmia and social behavior (∼360 observations per system) from 44 mothers and typically developing 9-month-old infants during a novel modified "still-face" (text message perturbation) task. Stochastic autoregression models indicate that the infant parasympathetic nervous system is coupled within and between people second by second and is sensitive to social context. Intraindividual, we found positive coupling between infants' parasympathetic nervous system activity and their social behavior in the subsequent second, but only during the moments and periods of active caregiver engagement. Between people, we found a bidirectional coregulatory feedback loop: Mothers' parasympathetic activity positively predicted that of their infant in the subsequent second, a form of synchrony that decreased during the text message perturbation and did not fully recover. Conversely, infant parasympathetic activity negatively predicted that of their mother at the subsequent second, a form of synchrony that was invariant over social context. Findings reveal unidirectional parasympathetic coupling within infants and a complementary allostatic feedback loop between mother and infant parasympathetic systems. They offer novel evidence of a dynamic, socially embedded parasympathetic system at previously undocumented timescales, contributing to both basic science and potential clinical targets to better support adaptive, multisystem social development. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Analysis of Convergence and the Scenarios of Economic Growth in Indonesia Using System Dynamic Approach

This study aims to determine whether there is sigma convergence and beta convergence in Indonesia, to determine the effect of electricity infrastructure, human development, and ICT on convergence of economic growth, and to determine the scenario that can accelerate economic growth in Indonesia. The data used in this study is secondary data. The methods used are convergence analysis, panel data regression analysis, and dynamic system approach. The results showed that there was sigma convergence and no beta convergence in Indonesia in 2013-2022. Electricity infrastructure, human development, and ICT have not been able to encourage convergence of economic growth with electricity infrastructure having a significant negative effect, human development having a significant positive effect, and ICT having an insignificant negative effect. Scenarios that can be done to accelerate economic growth are structural scenarios and parameter scenarios.

Entropy as a Window Into Behavioral Phase Transitions: Unveiling Contextual Dynamics in Affordance-Based Reaching.

Prior work has demonstrated the presence of hysteresis effects in the control of affordance-guided behavior, in that behavioral transitions around a critical action boundary vary with directions of change in said action boundary. To date, research on this topic has overlooked the influence of the global context on these phenomena. We employ an affordance-based reaching task, whereby participants were asked to move a target to a goal by passing through one of two apertures (size variable or size constant). It was found that the direction of change in the size of the variable aperture influenced the point of behavioral transitions, and this effect interacted with the location of a given goal. In addition, we considered fluctuations in the entropy of participants' reach trajectories as a window into the nature of the behavioral phase transitions. Differences in the structure of entropy were found depending on the direction of change in the size variable aperture. These results are discussed in light of a dynamical systems approach, and recommendations for future work are made.

Investigating the link between temperamental and motor development: a longitudinal study of infants aged 6–42 months

BackgroundSince the 1920s, motor development has been a strong research theme, focusing on infants' acquisition of motor skills, such as turning over and crawling. In the 1980s, a dynamic systems approach began emphasizing children's own motivation, which helped explain individual differences in the emergence of motor skills. However, few studies have examined factors contributing to individual differences in early motor development. In response, we investigated directional associations between temperament and motor development in children aged 6 months to 3 years.MethodThe Japan Environment and Children’s Study (JECS-A) recruited mothers between January 2011 and March 2014. 2,639 mothers were sent a questionnaire at 6 months, and responses were received from 1,657 of them, with full data for children aged 6 months, 2 years, and 3 years, including from three mothers of twins, were analyzed through structural equation modeling. Question items regarding fine and gross motor activities at each age were selected by pediatric neurologists specializing in developmental disorders. The Japanese version of the Little Developmental Coordination Disorder Questionnaire was administered at 42 months. Temperament was assessed through the parent-reported Behavior Questionnaire (short version) for infants, toddlers, and children. In all three measures, Surgency and Negative Affectivity were extracted, and Effortful Control, a major form of self-regulation, was found from toddlerhood onward, as in previous studies.ResultsA path diagram reveals that at 6 months, Surgency and Orienting/Regulation interacted positively with the motor function (respectively, r = .57; r = 40, ps < .001). Up to about 3 years, Effortful Control plays a role in facilitating the motor function, resulting in positive effects on Control During Movement (CDM), General Coordination (GC), and Fine Motor Movement (FMM) (β = 14; β = 30; β = 37, ps < .001). Surgency had a positive effect on CDM and GC (β = 18; β = 06, ps < .001), whereas Negative Affect had a negative influence on FMM and GC (β = -.08; β = -.08, ps < .001).ConclusionWhile Surgency may be a key reactive factor in early motor development, Effortful Control and Movement develop in an interactive manner.Trial registrationUMIN000030786.Scientific Title: The Japan Environment and Children’s Study.Date of disclosure of the study: 2018/01/15.Only questionnaires were administered in the study.

Seawater sulfate dynamics and a new tipping point in the Earth system

Seawater sulfate (SO42−) concentrations have changed by orders of magnitude in response to atmospheric and ocean redox dynamics throughout Earth’s history. A fundamental model that constrains seawater SO42− dynamics based on the principles of mass balance, however, is still lacking. Here, we used a dynamical systems approach to determine the effects of global source and sink strengths on seawater SO42− concentrations. Our stochastic analysis of the SO42− mass balance revealed two most probable seawater SO42− concentration ranges: one under widespread oceanic anoxic conditions with SO42− concentrations &amp;lt;1000 µM, and the other with SO42− concentrations around or above 10,000 µM under widely oxygenated ocean conditions. Swings between these two seawater SO42− concentration ranges are notably evident during the Phanerozoic Eon and developed in response to reoccurring oceanic anoxic events. We also identified a threshold for the extent of oceanic anoxia above which seawater SO42− concentrations collapse to &amp;lt;1000 µM, with corresponding impacts on global biogeochemical cycles, biology, and climate.

Quantum dynamics of wave packets in a Morse potential: A dynamical system approach.

We show how a dynamical systems approach can, somewhat unexpectedly, be relevant in the quantum dynamics featuring oscillations and escape in the Morse potential. We compare the dynamics resulting from the approach with the results obtained from a direct numerical integration of the relevant Schrödinger equation to support our claim. An interesting finding of the numerical investigation is the marked increase in the probability of obtaining a significant fraction (more than 50%) of the wave packet in the classically forbidden range beyond a critical energy of the packet. The fact that the dynamical systems approach shows an instability near that critical energy is a definite indication of the relevance of dynamical systems to the quantum dynamics. At lower energies, the calculated mean position 〈x〉 and variance V from the dynamical system allow us to clearly establish the phenomenon of tunneling since the sum 〈x〉+sqrt[V] clearly exceeds, at various times, the classical bound on displacement for the corresponding energy.

Mathematical analysis of the Wiener processes with time-delayed feedback

It is known that time delays generally make a system unstable. However, it is numerically observed that the diffusion coefficients of the Wiener processes with time-delayed feedback decrease while increasing the time delay τ. In particular, the decay of the diffusion coefficients with the form (11+τ)2 has been confirmed by numerical simulations [Ando et al., Phys. Rev. E 96, 012148 (2017)]. In this paper, we present two analytical derivations for the relation (11+τ)2 by dynamical system approaches using the Laplace transform and stochastic differential equations.

Enhancing e-government in digital transformation: integrating archive management and digital solutions in Pekanbaru, Indonesia

Efficient and modern archive management is very important in this digital era, especially at the local government level. In this context, this study explores the urgency of archive management using the Integrated Dynamic Archival Information System (SRIKANDI) approach in the Pekanbaru City Government. The research method used is qualitative, with data sources from interviews, documentation, and observation and analysis using the NVivo 12 Plus software. The study's results identified challenges to SRIKANDI implementation, including inadequate technological infrastructure, the need for skilled human resources in information technology, attention to data security, changes in organizational culture, and ongoing technical support. Based on these findings, policy recommendations have been made, including investments in technology infrastructure, human resource training and development, strict data protection, and changes in organizational culture. This research has positive implications for archive management, increasing efficiency and accountability in Pekanbaru. This research provides insights for other city governments wishing to undertake similar digital transformations in electronic-based archives management

Single droplet or bubble and its stability: Kinetic theory and dynamical system approaches.

Steady solutions of a single droplet or bubble in the van der Waals fluid are investigated on the basis of the kinetic model equationthat has been recently proposed by Miyauchi etal. [Gas Dynamics with Applications in Industry and Life Sciences (Springer, Cham, 2023), pp. 19-39]. Under the thermal equilibrium condition and isotropic assumption with respect to the origin of the coordinates, the kinetic equationis reduced to an ordinary differential equationfor the density, which can be regarded as a low-dimensional dynamical system. The possible density distribution is studied as a flow in the low-dimensional phase space. It is clarified that a single droplet or bubble can be understood as a flow that goes into a fixed point and that the flow is qualitatively different in the unstable and metastable parameter regions. The features of the obtained density distributions in individual regions are also clarified. Finally, the stability of those solutions is studied by direct numerical experiments of the kinetic equation.