Dynamical Systems Approach Research Articles

Dynamical Systems Analysis of f(Q) Gravity

Modified gravity theories can be used for the description of homogeneous and isotropic cosmological models through the corresponding field equations. These can be cast into systems of autonomous differential equations because of their sole dependence on a well-chosen time variable, be it the cosmological time, or an alternative. For that reason, a dynamical systems approach offers a reliable route to study those equations. Through a model-independent set of variables, we are able to study all f(Q) modified gravity models. The drawback of the procedure is a more complicated constraint equation. However, it allows the dynamical system to be formulated in fewer dimensions than using other approaches. We focus on a recent model of interest, the power-exponential model, and generalize the fluid content of the model.

A Dynamical Systems Approach to Machine Learning

Employing various mathematical tools in machine learning is crucial since it may enhance the learning problem’s efficiency. Dynamic systems are among the most effective tools. In this study, an effort is made to examine a kind of machine learning from the perspective of a dynamic system, i.e., we apply it to learning problems whose input data is a time series. Using the discretization approach and radial basis functions, a new data set is created to adapt the data to a dynamic system framework. A discrete dynamic system is modeled as a matrix that, when multiplied by the data of each time, yields the data of the next time, or, in other words, can be used to predict the future value based on the present data, and the gradient descent technique was used to train this matrix. Eventually, using Python software, the efficacy of this approach relative to other machine learning techniques, such as neural networks, was analyzed.

Cosmological dynamics of Cuscuta–Galileon gravity

We study cosmological dynamics of the Cuscuta–Galileon gravity with a potential term by using the dynamical system approach. This model is galileon generalization of the cuscuton gravity where we add a potential term to the theory in order to obtain the radiation and matter dominated eras. The exponential potential can provide the sequence of the thermal history of the Universe correctly, i.e. starting from radiation dominance, passing through matter dominant era, and then approaching de Sitter expansion stage. This model has no ghosts and the Laplacian instability for both scalar and tensor perturbations. We also discuss the observational constraints on the model parameters. It turns out that the model actually has three degrees of freedom unlike the original cuscuton theory.

Utilization of entire new dynamical system approach for peristalsis of Power law fluid with temperature-dependent viscosity

Peristalsis of non-Newtonian fluid with variable viscosity and viscous dissipation is considered in this paper. Modified Brinkman number highlighting both the variable viscosity and viscous dissipation is introduced. By utilizing the long wavelength and small Reynold number approximations, an analytical solution is obtained for stream function. The qualitative analysis is presented using the theory of dynamical system. The phase portraits representing topological structures like trapping, augmented flow and the backward flow are drawn. The change in qualitative flow patterns is discussed from the bifurcation diagrams. The exact size of the bolus is numerically determined. HIGHLIGHTS Analytical solution for Power law fluid with temperature-dependent viscosity. The theory of dynamical system is utilized for stability and bifurcation analysis. The topological structure of the flow is presented using bifurcation theory and phase plane analysis. The size of the bolus is calculated numerically.

Dynamical analysis in regularized 4D Einstein–Gauss–Bonnet gravity with non-minimal coupling

We investigate the regularized four-dimensional Einstein–Gauss–Bonnet (4DEGB) gravity with a non-minimal scalar coupling function, which is an extension of the regularized 4DEGB theory. By introducing non-minimal coupling to the Gauss-Bonnet term, we demonstrate the additional contribution to the dynamical equations which is otherwise absent in the dimensionally regularized theory. Furthermore, we analyze the stability of the system by using the dynamical system approach based on fixed points. Then, we consider time evolution to investigate the history of the universe and to constrain observational data to obtain the cosmological parameters of the model.

A periodic delay differential system for mosquito control with Wolbachia incompatible insect technique

Wolbachia incompatible insect technique (IIT) depends on releasing male-only Wolbachia-infected mosquitoes to reduce/eradicate wild type mosquito populations. Mathematical models can be utilized to help investigate the altered mosquito population dynamics under IIT and propose the appropriate releasing strategies. Incorporating seasonal temperature variations and larval competition, a delayed periodic stage structured model is formulated, which is essentially different from existing models since additional density-dependent death rate due to larval competition introduces a density-dependent survival probability of larvae. This novel feature brings new challenges to mathematical analysis and further model extension in studying the dynamics of mosquito borne diseases (MBDs). By assuming continuous proportional releasing strategies, threshold dynamics in terms of the basic offspring number R0 are established by employing the dynamical system approach. The mosquito population size is shown to either go extinction if R0<1 or stabilize at a periodic pattern when R0>1. Then, we numerically explore the seasonal effects on R0 and the impact of larval competition and released amount of Wolbachia-infected males under two levels of mosquito control objectives, i.e., population eradication and reduction. Overestimates of R0 are observed if seasonality is ignored. The ratio of released Wolbachia-infected males to wild type males (the overflooding ratio, pw) and larval competition are shown to play positive roles in reducing both the required time for population eradication and ultimate adult peak abundance. In particular, the initial population size is negatively correlated with the eradication time, which can be shorten to a minimum of 5 years. In summary, IIT alone may be difficult to eradicate/reduce the mosquito population. Other conventional mosquito control approaches such as spraying larvicides should be used in combination to efficiently control mosquitoes.

A Dynamical Systems Investigation of the Co-regulation between Perceived Daily Parental Warmth and Adolescent Attention-deficit/hyperactivity Disorder Symptoms.

Longitudinal research demonstrates that child ADHD symptoms and behaviors exhibit reciprocal associations with parenting behaviors over time. However, minimal research has investigated these associations and their dynamic links at the daily level. Intensive longitudinal data can disentangle stable between-person differences from within-person fluctuations and reveal nuanced short-term family dynamics on a micro timescale. Using 30-day daily diary data from a community sample of 86 adolescents (Mage = 14.5, 55% female, 56% White, 22% Asian) and latent differential equation modeling, this study examined the links between perceived daily parental warmth and ADHD symptoms as coupled dynamical systems. The results show that the magnitude of fluctuations in perceived daily parental warmth generally remains stable, while elevated ADHD symptoms return to their normal level over time. Perceived parental warmth is sensitive to change in ADHD symptoms such that adolescents feel that their parents will fine-tune their warmth with gradual changes when adolescents demonstrate heightened symptoms. There are substantial between-family differences in these regulating system dynamics. Among families with more baseline parental non-harsh discipline, both perceived parental warmth and ADHD symptoms tend to be more stable and fluctuate less often. Intensive longitudinal data and dynamical systems approaches offer a new lens to uncover short-term family dynamics and adolescent adjustment at a refined micro level. Future research should explore antecedents and consequences of between-family differences in these short-term family dynamics on multiple timescales.

Two repelling random walks on [formula omitted

We consider two interacting random walks on Z such that the transition probability of one walk in one direction decreases exponentially with the number of transitions of the other walk in that direction. The joint process may thus be seen as two random walks reinforced to repel each other. The strength of the repulsion is further modulated in our model by a parameter β≥0. When β=0 both processes are independent symmetric random walks on Z, and hence recurrent. We show that both random walks are further recurrent if β∈(0,1]. We also show that these processes are transient and diverge in opposite directions if β>2. The case β∈(1,2] remains widely open. Our results are obtained by considering the dynamical system approach to stochastic approximations.

A Dynamical Systems Approach to the Theory of Circumbinary Orbits in the Circular Restricted Problem

To better understand the orbital dynamics of exoplanets around close binary stars, i.e., circumbinary planets (CBPs), we applied techniques from dynamical systems theory to a physically motivated set of solutions in the Circular Restricted Three-Body Problem (CR3BP). We applied Floquet theory to characterize the linear dynamical behavior—static, oscillatory, or exponential—surrounding planar circumbinary periodic trajectories (limit cycles). We computed prograde and retrograde limit cycles and analyzed their geometries, stability bifurcations, and dynamical structures. Orbit and stability calculations are exact computations in the CR3BP and reproducible through the open-source Python package pyraa. The periodic trajectories (doi.org/10.5281/zenodo.7532982) produce a set of noncrossing, dynamically cool circumbinary orbits conducive to planetesimal growth. For mass ratios μ ∈ [0.01, 0.50], we found recurring features in the prograde families. These features include (1) an innermost near-circular trajectory, inside which solutions have resonant geometries, (2) an innermost stable trajectory (a c ≈ 1.61 − 1.85 a bin) characterized by a tangent bifurcating limit cycle, and (3) a region of dynamical instability (a ≈ 2.1 a bin; Δa ≈ 0.1 a bin), the exclusion zone, bounded by a pair of critically stable trajectories bifurcating limit cycles. The exterior boundary of the exclusion zone is consistent with prior determinations of a c around a circular binary. We validate our analytic results with N-body simulations and apply them to the Pluto–Charon system. The absence of detected CBPs in the inner stable region, between the prograde exclusion zone and a c , suggests that the exclusion zone may inhibit the inward migration of CBPs.

A dynamical model of visual motion processing for arbitrary stimuli including type II plaids

To explore the operating principle of visual motion processing in the brain underlying perception and eye movements, we model the information processing of velocity estimate of the visual stimulus at the algorithmic level using the dynamical system approach. In this study, we formulate the model as an optimization process of an appropriately defined objective function. The model is applicable to arbitrary visual stimuli. We find that our theoretical predictions qualitatively agree with time evolution of eye movement reported by previous works across various types of stimulus. Our results suggest that the brain implements the present framework as the internal model of motion vision. We anticipate our model to be a promising building block for more profound understanding of visual motion processing as well as for the development of robotics.

Development of brain state dynamics involved in working memory.

Human functional brain networks are dynamically organized to enable cognitive and behavioral flexibility to meet ever-changing environmental demands. Frontal-parietal network (FPN) and default mode network (DMN) are recognized to play an essential role in executive functions such as working memory. However, little is known about the developmental differences in the brain-state dynamics of these two networks involved in working memory from childhood to adulthood. Here, we implemented Bayesian switching dynamical systems approach to identify brain states of the FPN and DMN during working memory in 69 school-age children and 51 adults. We identified five brain states with rapid transitions, which are characterized by dynamic configurations among FPN and DMN nodes with active and inactive engagement in different task demands. Compared with adults, children exhibited less frequent brain states with the highest activity in FPN nodes dominant to high demand, and its occupancy rate increased with age. Children preferred to attain inactive brain states with low activity in both FPN and DMN nodes. Moreover, children exhibited lower transition probability from low-to-high demand states and such a transition was positively correlated with working memory performance. Notably, higher transition probability from low-to-high demand states was associated with a stronger structural connectivity across FPN and DMN, but with weaker structure-function coupling of these two networks. These findings extend our understanding of how FPN and DMN nodes are dynamically organized into a set of transient brain states to support moment-to-moment information updating during working memory and suggest immature organization of these functional brain networks in childhood, which is constrained by the structural connectivity.

A study on the bifurcation of the peristaltic driven flow of Ellis fluid

In this work, a bifurcation analysis is presented for the transport of Ellis fluid model due to peristaltic activity. The position, qualitative nature and bifurcations of stagnation-points are deliberated through the dynamical system approach. An exact expression for stream function is found by using the lubrication approach. Based on the stream function, a system of autonomous differential equations is established to analyze the equilibrium-points. Three kinds of flows are observed, namely backward flow, trapping and augmented flow. The transition of one flow into other represents a bifurcation. In the first bifurcation, a saddle point bifurcates into two centers in the normal direction while the second bifurcation emerges where nearby saddle nodes join under the wave trough and then split into two branches in the transverse direction. Ramifications of different embedded parameters on the bifurcations and nature of stagnation-points are explored through graphical representations. It is found that bifurcations transpire earlier for viscous fluids as compared to shear-thinning fluids. Further, bifurcations appear at low flow rate for small values of the material parameter . Moreover, in Newtonian fluids, as opposed to shear-thinning fluids, the trapping starts earlier and the backward region expands for larger values of the material parameter .

Cosmology in f(Q) gravity: A unified dynamical systems analysis of the background and perturbations

Motivated by the fact that cosmological models based on $f(Q)$ gravity are very efficient in fitting observational datasets at both background and perturbation levels, we perform a combined dynamical system analysis of both background and perturbation equations in order to examine the validity of this result through an independent method. We examine two studied $f(Q)$ models of the literature, namely the power-law and the exponential ones. For both cases, we obtain a matter-dominated saddle point characterized by the correct growth rate of matter perturbations, followed by the transition to a stable dark-energy dominated accelerated universe in which matter perturbations remain constant. Furthermore, analyzing the behavior of $f \sigma_8$, we find that the models fit observational data successfully, obtaining a behavior similar to that of $\Lambda$CDM scenario, although the exponential model does not possess the latter as a particular limit. Hence, through the independent approach of dynamical systems, we do verify the results of observational confrontation, namely that $f(Q)$ gravity can be considered as a very promising alternative to the $\Lambda$CDM concordance model.

The attributes of the dust-acoustic solitary and periodic structures in the Saturn's inner magnetosphere

Nonlinear characteristics of dust-acoustic (DA) structures including the localized and periodic waves in a plasma having Maxwellian ions and superthermal two-temperature electrons are investigated. The wave equations, including both Kadomtsev–Petviashvili (KP) and modified KP (mKP) equations, are derived using the reductive perturbation technique (RPT). The quantitative and qualitative characteristics of both compressive and rarefactive structures are studied. The Jacobi elliptic function expansion method (JEFEM) is employed for the purpose of quantitative analysis, while the qualitative behavior is studied by the dint of the dynamical system approach. The solutions to the mKP equation hold under a critical condition where the quadratic nonlinearity ceases to exist. It is noticed that the KP equation admits only rarefactive solitary waves (SWs), whereas the mKP equation admits both compressive and rarefactive SWs. It is found that the profile (amplitude and width) of both DA solitary and periodic structures are different at different radii of Saturn's inner magnetosphere. The effect of the kappa spectral index is studied, and it is found that when the population of energetic cold electrons is decreased, the solitary structure gets energized. Our study is applied to Saturn's inner magnetosphere where kappa distributed two-temperature electrons and dust grains with negative charge are observed by various satellite missions.

Unsuccessful Accommodations: Reconceptualizing the Psychopathology Attributed to Neuropsychological Deficits

This contribution proposes reframing the concept of psychopathology as it applies to the dysfunctions that individuals with neuropsychological deficits display. It suggests that labeling these dysfunctions as symptoms of an underlying condition is an incomplete way of characterizing the process that leads to that outcome. An evolutionary and nonlinear dynamic systems approach complements this position and depathologizes individuals’ efforts to deal with their disabilities. The proposed modification introduces the concept of unsuccessful accommodations to characterize these individuals’ efforts to deal with their deficits.

REVIEW OF URBAN GREENING POLICY IN INDONESIA: A CASE STUDY IN JAKARTA PROVINCE

Urban greening schemes in Indonesia have experienced various challenges in providing quality green open space in sufficient quantities and need for a more appropriate scheme. In this case, the policy aspect is presumed to inhibit optimizing the provision and utilization of green open space in Indonesia. This study uses descriptive qualitative method that aims to analyze policy aspects related to the provision of green open space in large and dense urban areas with a case study Jakarta. It provides a basic analysis scheme to find the root cause of the urban greening schemes issue in Indonesia. The result shows that the provision of green open space has been mandated in various regulations and policies on a local to global scales. However, law enforcement efforts in implementing these policies and regulations require integrated and comprehensive endeavors to respond to the complexity of the public policy system related to the provision of green open space. In conclusion, this study needs an in-depth research to find complex and dynamic components associated with the complexity of providing green open space with a dynamic system approach. Keywords: Urban Greening Scheme; Law enforcement, Dynamic complexity

Bifurcations and exact traveling wave solutions of the (n+1)-dimensional q-deformed double sinh-Gordon equations

&lt;p style='text-indent:20px;'&gt;We consider an (n+1)-dimensional q-deformed double sinh-Gordon equation. The dynamical system approach is employed to study the model problem, from which we are able to obtain all possible bounded solutions, such as solitary wave solutions, kink and anti-kink wave solutions, and periodic wave solutions under different parameter conditions. Eleven exact parametric representations are provided explicitly.&lt;/p&gt;

Dynamical behavior of traveling waves in a generalized VP-mVP equation with non-homogeneous power law nonlinearity

&lt;abstract&gt;&lt;p&gt;In this paper, we investigate the dynamical behavior of traveling waves for a generalized Vakhnenko-Parkes-modified Vakhnenko-Parkes (VP-mVP) equation with non-homogeneous power law nonlinearity. By the dynamical systems approach and the singular traveling wave theory, the existence of all possible bounded traveling wave solutions is discussed, including smooth solutions (solitary wave solutions, periodic wave solutions and breaking wave solutions) and non-smooth solutions (solitary cusp wave solutions and periodic cusp wave solutions). We not only obtain all the explicit parametric conditions for the existence of 5 kinds of bounded traveling wave solutions, but also give their exact explicit expressions. Moreover, we qualitatively analyze the dynamical behavior of these traveling waves by using the bifurcation of phase portraits under different parameter conditions, and strictly prove the evolution of different traveling waves with their exact expressions.&lt;/p&gt;&lt;/abstract&gt;

Analysis system dynamic of chicken egg production system: Case in West Sumatra Indonesia

A policy study is needed to guide the planning process to develop a sustainable agropolitan area for laying hens in Limapuluh Kota Regency. This research aims to design a policy for developing sustainable laying hen businesses through modeling the chicken egg production system. The dynamic systems approach was used to determine the production system for chicken egg production, which consists of two sub-systems: the layer chicken population sub-system and the business profit sub-system. Each sub-system interacts dynamically based on time. The research results reveal that the chicken egg production model in Limapuluh Kota Regency is accurate and can be used for decision-making activities. The model and its development can help determine the direction of chicken egg production policy to be developed into a sustainable agropolitan area. In the future, overall chicken egg production in Limapuluh Kota Regency is likely to increase, leading to an increase in profits for the egg-laying chicken farming business. However, an increase in feed prices without a corresponding increase in egg prices may hamper the rate of increase in egg.

BIFURCATIONS AND OBTAINED EXACT SOLUTIONS OF THE OPTICAL SOLITON MODEL IN METAMATERIALS DOMINATED BY ANTI-CUBIC NONLINEARITY

In this paper, we study the optical model in metamaterials with nonlinear influence of non-Kerr law and a few Hamiltonian perturbation terms. The nonlinearity of metamaterials is dominated by anti-cubic type. We apply the approach of dynamical system to find the travelling wave solutions of the optical model. Under different parameter conditions, bifurcations of phase portraits and exact periodic solutions, homoclinic and heteroclinic solutions, peakon, periodic peakons as well as compacton solutions for this planar dynamical system are given. By using the first integral, exact solutions of can be calculated under different parameter conditions. 83 exact explicit parametric representations are derived.