Dynamical Systems Approach Research Articles

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.

Modelling motion energy in psychotherapy: A dynamical systems approach.

In this study we introduce an innovative mathematical and statistical framework for the analysis of motion energy dynamics in psychotherapy sessions. Our method combines motion energy dynamics with coupled linear ordinary differential equations and a measurement error model, contributing new clinical parameters to enhance psychotherapy research. Our approach transforms raw motion energy data into an interpretable account of therapist-patient interactions, providing novel insights into the dynamics of these interactions. A key aspect of our framework is the development of a new measure of synchrony between the motion energies of therapists and patients, which holds significant clinical and theoretical value in psychotherapy. The practical applicability and effectiveness of our modelling and estimation framework are demonstrated through the analysis of real session data. This work advances the quantitative analysis of motion dynamics in psychotherapy, offering important implications for future research and therapeutic practice.

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).

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.

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.

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.

New features of circular geodesics in Kalb–Ramond gravity: an autonomous dynamical system approach

Kalb–Ramond gravity is expected to show the signatures of the low energy limit of the Lorentz violating extension of the standard model of particle physics. To understand the theory further, we study the circular geodesics belonging to a class of exact solutions [found recently by Lessa, Silva, Maluf, Almeida (LSMA)] by posing them as a Hamiltonian dynamical autonomous system. The analysis on the phase space for relevant values of the Lorentz violating parameters reveals for the first time a wealth of novel information that include prediction of homoclinic orbits, saddle points, separatrices that are not available from the conventional analysis. Their image on the actual physical space is discussed.

Insights from a dynamical system approach into the history of atmospheric oxygenation

Atmospheric oxygen levels are traditionally viewed to have been relatively stable throughout Earth’s history with several-step increases. Emerging evidence, however, suggests extremely dynamic atmospheric oxygen levels through large swaths of Earth’s history. Here, we provide a new perspective on atmospheric oxygen evolution using a dynamical analysis to explore the relative importance of previously proposed feedbacks on the global oxygen and carbon cycles. Our results from a stochastic analysis of oxygen mass balance in this framework suggest there are multiple steady states for atmospheric oxygen, but only three stable states. One stable state under anoxic conditions (<10−5 present atmospheric level (PAL)), one at low (~10−3to 10−2 PAL), and one near modern value atmospheric oxygen levels. Our findings also suggest two unstable states (tipping points) for atmospheric oxygen: one around 10−5 and another one around 10−1 PAL.

Parsimonious streamflow forecasting system based on a dynamical systems approach

Operational hydrologic forecasting often relies on the use of physically-based computer models at the catchment scale. However, our understanding of streamflow generation is still evolving and incomplete, and oftentimes linearization assumptions must be made to make physically-based hydrologic and hydraulic models tractable. In addition to uncertainty in the physical runoff-generation mechanisms, many physically-based approaches do not formally assimilate observed streamflow data. Streamflow is their output, deterministically simulated from observed inputs (such as precipitation, temperature, etc.). Divergences between observed and simulated streamflow may be due to input uncertainty, calibration issues, or problems with the inherent physical process representation. Thus, data-driven approaches that are responsive to observed streamflow by including assimilation as an essential feature are promising in operational hydrology. In this study, we use a novel forcings-weighted k-Nearest Neighbor (kNN) nonlinear timeseries forecasting method developed in the context of the modeling of nonlinear dynamical systems. The rainfall-runoff transform is assumed to be a low-dimensional system of (unknown) nonlinear differential equations; the deterministic state space is reconstructed based on the streamflow timeseries; and a forecast is generated based on how “similar” the current hydrograph is to historical events encoded within the reconstructed state space, weighted by the similarity of forcings. We tested the model in a long-term test period with no real data assimilation, and in forecast mode with daily data assimilation. When used for forecasting, we also illustrate two different uncertainty quantification approaches: forecast postprocessing and internal-to-the-model ensemble generation. The method is conceptually and computationally simple, but offers promising results. We tested the model in three different scenarios. First, investigating a long-term test period with no real data assimilation in a rainfall-dominated research catchment at the Coweeta Hydrologic Lab in North Carolina, USA. The simulation exhibited an NSE of 0.73. Next, we included a conceptual snowmelt model to drive the long term simulation and studied boreal-temperate transition zone catchments in northern Minnesota, USA. The study area included a small (<0.1 mi2) reference research catchment at the Marcell Experimental Forest, and a large river basin (>19 k mi2) with incomplete forcings information. The kNN method yielded NSEs from 0.28 to 0.50. And finally, we conducted a pseudo-operational forecasting test for a large river basin in northern Minnesota, USA with a focus on performance forecasting a flood-of-record on the Rainy River. The test involved reforecasting, data assimilation, and implementation of ensemble and postprocessing bias correction uncertainty-quantification schemes. The technique demonstrated good performance capturing a flood-of-record on a large catchment (−5.7 to −3.3 % crest error with 1-day of lead time). For the entire test period in forecast mode, the 1-day lead time NSE was 0.99, going down to 0.79 for the 7-day lead time, showing its general utility as an operational forecasting tool.

Numerical analysis of coupled dynamical biological networks: Modeling electrical information exchange among nerve cells using finite volume method

An innovative approach to modeling the conduction of electrical impulses via intricate neuronal structures is introduced in this paper, which offers a theoretical and computational examination of parameter estimation in a coupled FitzHugh–Nagumo model. With this goal in mind, we present a finite volume approach to solving the FitzHugh–Nagumo model and check the numerical method’s accuracy against previous findings. To further assess and contrast the efficacy and precision of the model’s outputs, a finite difference formulation is incorporated. To clarify the basic qualitative properties of the inhibitor–activator mechanism intrinsic to the coupled FitzHugh–Nagumo model, the analysis uses dynamical system approaches and linear stability analysis. The results show that the suggested schemes are very accurate, with conditional stability, reaching fourth-order spatial and second-order temporal precision. The results are given in both tabular and graphical forms. According to numerical results, the suggested finite volume method outperforms the finite difference method in accurately and efficiently solving the nonlinear coupled FitzHugh–Nagumo model. Neuronal activity and electrical communication are complex biological systems with a lot of investigated nonlinear differential equations; this research helps us understand more about these topics.

OPTIMIZATION OF WASTE MANAGEMENT IN SUMBAWA DISTRICT USING A DYNAMIC SYSTEM MODEL

The main problem that occurs in society today apart from basic needs is the problem of waste. This waste problem certainly needs a solution in good, effective, sustainable and long-term management. The waste issue not only occur in big cities but also in developing areas. Sumbawa Regency as one of the regions that continues to develop and grow requires optimum and long-term planning of solid waste management and systems. In 2021, the waste handled in Sumbawa Regency will only be around 17.5% of the total waste. This shows that the waste management system in Sumbawa Regency is not optimal. Optimal waste management can be achieved by taking an academic approach through model development. One such model is the dynamic system model. This can describe the causal relationship between variables that affect solid waste problems and to provide an overview of the waste management system through simulations based on the factors that influence the processing model. Therefore, it is necessary to develop an optimization model for waste management specifically in Sumbawa Regency using a dynamic systems approach. The purpose of this study is to describe waste management in the form of an optimization model for waste management in Sumbawa Regency with a dynamic system. Optimization results show that the optimistic model yields a total of 127.01 tons/day, the moderate model yields a total of 98.23 tons/day and the pessimistic model produces 62.5 tons/day

Design of stochastic computational Levenberg Marquardt backpropagation-based technique to investigate temperature distribution of longitudinal moving porous fin

The improvement of thermal exchange is of utmost interest in a wide range of engineering areas. The current study focuses on thermal evaluation involving natural radiation and convection in a fractionally arranged moving longitudinal fin model placed under a magnetic field. We implement the Levenberg Marquardt backpropagation (LMB) algorithm for investigating an innovative use of stochastic numerical computation for analyzing the efficiency of the temperature distribution in a porous moving longitudinal fin. The datasets for LMB have been created using a shooting approach for dynamic systems with varying ranges of different parameters. The validation, testing, and training processes are used to simulate networks using the LMB approach for diverse scenarios of moving porous fin models. The reliability of results is assessed based on the regression measures, absolute error, error histograms, mean square error, and other metrics for fuller numerical modeling of the suggested LMB to investigate the thermal efficiency and effectiveness of porous moving fin.

A tool to assess early motor skill development: A study of Danish health visitors’ practice

In Denmark, health visitors play a crucial role in identifying early motor skill difficulties. In 74 % of the Danish municipalities, they use a motor skill assessment tool for infants aged 9–11 months, consisting of evaluating nine motor milestones. The assessment results in one of three remarks: 'age-appropriate motor development', ‘heightened attention required', or 'intervention needed'. This article aims to: 1) determine the relative importance of each milestone in the overall assessment score, 2) investigate the consistencies in test usage across municipalities, and 3) explore factors influencing health visitors' assessments. This mixed methods study utilizes questionnaires and interviews with health visitors from two municipalities. Findings indicate a general consistency in the importance of each motor milestone in both municipalities, with the exception of the milestone 'chews food with a coarser consistency and takes an interest in eating by him/herself.' The health visitors also consider the achievement of the nine-motor milestones more important as the child gets older. Health visitors in both municipalities follow a uniform approach, emphasizing continuous child development over specific motor milestone achievement. They also consider factors like interaction, sensory perception, overall and social development, and the joy of movement, which are not part of the formal assessment. This illustrates that the health visitors have a dynamic system approach to testing motor development, broadening the motor assessment beyond the tool's milestones.