Volterra Model Research Articles

Retraction Note: Coopetition analysis in industry upgrade and urban expansion based on fractional derivative gray Lotka–Volterra model

Retraction Note: Coopetition analysis in industry upgrade and urban expansion based on fractional derivative gray Lotka–Volterra model

Novel Framework for Exploring Human–Water Symbiosis Relationship: Analysis, Quantification, Discrimination, and Attribution

There is an interdependent symbiotic relationship between humans and water; scientific and effective assessment of the human–water symbiosis relationship is of great significance for the promotion of sustainable development. This study developed a novel framework of the human–water symbiosis relationship under an integrated perspective, which included theoretical interpretation, quantitative assessment, pattern discrimination, and an attribution analysis. Based on the symbiosis theory, the theoretical analysis of the human–water relationship was carried out to analyze the three basic elements of the human–water system, and then the evaluation index system of the human–water symbiosis system was constructed to quantitatively assess the development level of the human system and the water system. The Lotka–Volterra model was used to identify the symbiotic pattern, and the human–water symbiosis index was calculated to characterize the health state of the human–water symbiosis system. The main influencing factors of the human–water symbiosis system were further identified through an attribution analysis. Finally, a case study was carried out with 18 cities in Henan Province. Results reveal that (a) the proposed method can effectively realize the quantitative characterization of the human–water symbiosis relationship, with good applicability and obvious advantages; (b) the human–water symbiosis pattern of cities in Henan Province is dominated by the “human system parasitizes water system (H+W−)” pattern, and more attention should be paid to the water system in the subsequent development of it; and (c) the main factors influencing the human system, the water system, and the human–water symbiosis system are the research and development (R&D) personnel equivalent full-time (H7), per capita water resources (W1), and proportion of water conservancy and ecological water conservancy construction investment (W6), respectively. The findings can provide theoretical and methodological support for the study of the human–water symbiosis relationship and sustainable development in other regions.

Behavioral modeling of LMBA with different back‐off state using PSO optimized XGBoost method

AbstractIn this paper, an optimization technique based on the particle swarm optimization (PSO) algorithm is applied to the eXtreme gradient boosting (XGBoost) method for load modulated balanced amplifiers (LMBAs) modeling, taking into consideration both strong nonlinearity and memory effects. An overview of the basic principles of the proposed modeling technique is provided, as well as a detailed description of how the model is extracted. To improve the performance of the XGBoost model, the hyperparameters are optimized using the PSO algorithm. An in‐house designed LMBA was used to perform experimental validation, which demonstrated that the new PSO‐XGBoost model provided very efficient and extremely accurate predictions, especially in the case of strong nonlinearities. When compared to traditional Volterra models, canonical piecewise‐linear based models, and standard XGBoost models, the proposed PSO‐XGBoost model provides improved performance with reasonable complexity.

Feedback classification and optimal control with applications to the controlled Lotka–Volterra model

Let M be a σ-compact C ∞ manifold of dimension n ≥ 2 and consider a single-input control system: x ˙ ( t ) = X ( x ( t ) ) + u ( t ) Y ( x ( t ) ) , where X, Y are C ∞ vector fields on M. We prove that there exists an open set of pairs ( X , Y ) for the C ∞ -Whitney topology is such that they admit singular abnormal rays so that the spectrum of the projective singular Hamiltonian dynamics is feedback invariant. This result is applied to the controlled Lotka–Volterra dynamics, where such rays are related to shifted equilibria of the free dynamics.

Interspecific competition enhances microcystin production by Microcystis aeruginosa under the interactive influences of temperature and nutrients

Global warming and eutrophication contribute to frequent occurrences of toxic algal blooms in freshwater systems globally, while there is a limited understanding of their combined impacts on toxin-producing algal species under interspecific competitions. This study investigated the influences of elevated temperatures, lights, nutrient enrichments and interspecific interactions on growth and microcystin (MC) productions of Microcystis aeruginosa in laboratory condition. Our results indicated that elevated temperatures and higher nutrient levels significantly boosted biomass and specific growth rates of Microcystis aeruginosa, which maintained a competitive edge over Chlorella sp. Specifically, with phosphorus levels between 0.10 and 0.70 mg P L−1, the growth rate of Microcystis aeruginosa in mixed cultures increased by 23 %–52 % compared to mono-cultures, while the growth rate of Chlorella sp. shifted from positive in mono-cultures to negative in mixed cultures. Redundancy and variance partition analyses suggested that Chlorella sp. stimulate MC production in Microcystis aeruginosa and nutrient levels outshine temperature for toxin productions during competition. Lotka‒Volterra model revealed a positive correlation between the intensities of competitions and MC concentration. Our findings indicate that future algal bloom mitigation strategies should consider combined influence of temperature, nutrients, and interspecific competition due to their synergistic effects on MC productions.

Research on the Impact of Lamprey's Sex Ratio on Ecosystems Based on the Lotka-Volterra Model

The aim of this study is to explore the impact of the population of the Lamprey on the ecosystem, particularly through the regulation of sex ratio, in order to provide effective strategies for environmental control. The study first improved the traditional Lotka Volterra model by introducing predator-prey relationships and environmental limiting factors. A Lotka Volterra predator environment model was established, and the stable environment of lampreys and their parasitic fish was simulated using this model. The results indicate that lower gender ratios (male population/overall population) can cause greater harm to the environment. The change in gender ratio can help control the food chain and may also exacerbate resource competition. Further integrating the relationship between gender ratio and growth rate into the Lotka Volterra predator environment model to form a gender Lotka Volterra predator environment model, the study found that a smaller gender ratio can lead to a decrease in ecological stability. When the gender ratio reaches a critical value, the ecosystem collapses. In addition, a dynamic ecosystem model was constructed for five species of organisms, including lampreys and parasites. Simulation results showed that reducing the sex ratio of lampreys can inhibit parasites and promote the prosperity of other organisms. The model has high robustness and stability. This study indicates that by regulating the sex ratio of lampreys, their impact on the ecosystem can be effectively controlled, providing a feasible environmental intervention strategy.

Competition and edge effect in wildlife zoonotic agents

The Land-use change emerges as a fundamental factor in the increase in zoonotic diseases, affecting both ecosystems and human populations. The edge effect between forested areas and their surrounding environments, modifies species distribution, and consequently the dynamics zoonotic wildlife. Patches with high perimeter-to-area ratios may experience a more pronounced edge effect, justifying the relevance of studying patch shape in a disease dynamics. In addition, competition between species, especially between those that act as reservoirs and those that do not, plays a crucial role in eco-epidemiological dynamics. In this context, our study addresses competition dynamics between two species employ the Lotka–Volterra model. We introduce an internal classification in the host species with two compartments, susceptible and infected, and model the disease transmission rate using a function linked to parameters associated with the edge effect. Specifically, the transmission rate differentiates interactions between susceptible and infected individuals in the core area and the edge of the patch, being a function dependent on the shape index of the patch, and is of the edge effect and host density. We predicted that, although competition can decrease the spread of the disease among hosts, the edge effect can paradoxically increase it.

Investigation of the accuracy of integral models of the oculo-motor system

For mathematical modeling of the human oculomotor system (OMS), integral nonlinear models are used, which simultaneously take into account the nonlinear and inertial properties of the research object. Based on the data of experimental studies of the OMS "input-output", transient and diagonal intersections of transient functions of the second and third orders are determined. To obtain experimental data, an innovative eye tracking technology is used, which allows recording eye responses to test visual stimuli. Thus test signals are displayed on the computer monitor at different distances from the starting position in the horizontal direction. The aim of the research is to study the accuracy of OMS identification using eye-tracking data by evaluating the calculation errors of multidimensional transient functions when using methods of nonlinear dynamic identification based on models in the form of Volterra series and polynomials. The object of the study is the process of nonparametric identification of the OMS based on Volterra models in the time domain. The subject of the research is algorithmic and software tools for calculating the dynamic characteristics of OMS based on eye-tracking data, analyzing the accuracy of the obtained models using two identification methods: the approximation method and the least squares method (LSM). The means of nonlinear dynamic identification of the human OMS based on Volterra series and polynomials were developed in the Python programming environment. The accuracy estimates of various OMS (linear, quadratic, and cubic) models were obtained based on data from three responses to test signals of different amplitudes. For the same test signals, the same models in the form of the Volterra series and polynomials were obtained, as these models coincide in the region of convergence of the Volterra series. The analysis of errors in the assessment of the dynamic characteristics of the OMS demonstrated that the model in the form of an integral polynomial of the second degree, which was built using the LSM based on three responses, has an accuracy twice as high as the accuracy of similar models built using the data of two responses. Thus, in further studies of the psychophysiological state of a person based on nonlinear dynamic models of the OMS according to the data of three responses, it is advisable to use a model in the form of a quadratic Volterra polynomial. Figs.: 17. Tabl. 3. Refs.: 10 titles.

Heterogeneous mean-field analysis of the generalized Lotka–Volterra model on a network

Abstract We study the dynamics of the generalized Lotka–Volterra model with a network structure. Performing a high connectivity expansion for graphs, we write down a mean-field dynamical theory that incorporates degree heterogeneity. This allows us to describe the fixed points of the model in terms of a few simple order parameters. We extend the analysis even for diverging abundances, using a mapping to the replicator model. With this we present a unified approach for both cooperative and competitive systems that display complementary behaviors. In particular we show the central role of an order parameter called the critical degree, g c . In the competitive regime g c serves to distinguish high degree nodes that are more likely to go extinct, while in the cooperative regime it has the reverse role, it will determine the low degree nodes that tend to go relatively extinct.

Dynamic food web model based on Lotka Volterra model

Dynamic food web model based on Lotka Volterra model

Early warning signals of complex critical transitions in deterministic dynamics

Early Warning Signals (EWS) have generated much excitement for their potential to anticipate transitions in various systems, ranging from climate change in ecology to disease staging in medicine. EWS hold particular promise for bifurcations, a transition mechanism in which a smooth, gradual change in a control parameter of the system results in a rapid change in system dynamics. The predominant reason to expect EWS is because many bifurcations are preceded by Critical Slowing Down (CSD): if assuming the system is subject to continuous, small, Gaussian noise, the system is slower to recover from perturbations closer to the transition. However, this focus on warning signs generated by stochasticity has overshadowed warning signs which may already be found in deterministic dynamics. This is especially true for higher-dimensional systems, where more complex attractors with intrinsic dynamics such as oscillations not only become possible—they are increasingly more likely. The present study focuses on univariate and multivariate EWS in deterministic dynamics to anticipate complex critical transitions, including the period-doubling cascade to chaos, chaos-chaos transitions, and the extinction of a chaotic attractor. In a four-dimensional continuous-time Lotka–Volterra model, EWS perform well for most bifurcations, even with lower data quality. The present study highlights three reasons why EWS may still work in the absence of CSD: changing attractor morphology (size, shape, and location in phase space), shifting power spectra (amplitude and frequency), and chaotic transitional characteristics (density across attractor). More complex attractors call for different warning detection methods to utilise warning signs already contained within purely deterministic dynamics.

A Study on Effects of Species with the Adaptive Sex-Ratio on Bio-Community Based on Mechanism Analysis and ODE

The species of the adaptive male–female sex ratio has different effects on the bio-community. This paper is aimed at figuring out these effects through mechanism analysis and Ordinary Differential Equation (ODE). Hence, the ODE environmental model is created by combining the Lotka–Volterra model, the interspecific model, and other external factors. The stability is used to characterize these effects. According to this model, effects on bio-community stability under different male–female sex ratios are roughly observed. By innovatively considering different living environments during the species’ lifecycle, the ODE environmental model is optimized, and the effects of different male–female sex ratios on the bio-community are further analyzed by phase-track maps and relative standard deviation. It is found that there are different findings and features in resource-rich and resource-scarce living environments during the lifecycle. Meanwhile, bio-communities in these two types of environments are in a stable state based on different male–female sex ratios. Based on these findings, directive opinions can be used to manage and help relevant bio-communities.

Global dynamics of a diffusive competitive Lotka–Volterra model with advection term and more general nonlinear boundary condition

We investigate a competitive diffusion–advection Lotka–Volterra model with more general nonlinear boundary condition. Based on some new ideas, techniques, and the theory of the principal spectral and monotone dynamical systems, we establish the influence of the following parameters on the dynamical behavior of system (1.2): advection rates αu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\alpha _{u}$\\end{document} and αv\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\alpha _{v}$\\end{document}, interspecific competition intensities cu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$c_{u}$\\end{document} and cv\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$c_{v}$\\end{document}, the resources functions ru\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$r_{u}$\\end{document} and rv\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$r_{v}$\\end{document} of the two competitive species, and nonlinear boundary functions g1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$g_{1}$\\end{document} and g2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$g_{2}$\\end{document}. The models of (Tang and Chen in J. Differ. Equ. 269(2):1465–1483, 2020; Zhou and Zhao in J. Differ. Equ. 264:4176–4198, 2018) are particular cases of our results when gi≡const\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$g_{i}\\equiv const$\\end{document} for i=1,2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$i=1,2$\\end{document}, and hence this paper extends some of the conclusions from (Tang and Chen in J. Differ. Equ. 269(2):1465–1483, 2020; Zhou and Zhao in J. Differ. Equ. 264:4176–4198, 2018).

Influencia del uso de refugios por las presas en el modelo de depredación de Volterra

In various previous works, different predation models have been analyzed considering the use of refuge by the prey population, without carrying out an exhaustive analysis of its dynamics. In some of them it is stated that the use of shelters or dens by a fraction of the prey population has a stabilizing effect on predator-prey interaction. One of the objectives of this work is to show that some of these new systems considering refuge may have the same topological portrait in the phase plane as the original; but in others the dynamics change strongly. In our research we will introduce modifications to the well-known Volterra model, considering various ways to express the number of prey in refuge. In several of them, local dynamics equivalent to the original model are obtained, confirming that results reported as new were previously known based on the original system, without taking into account the refuge of the prey. We conclude that the behavior of the systems depends on the mathematical expression to describe the number of sheltered prey.

An SD-LV Calculation Model for the Scale of the Urban Rail Transit Network

The planning for the scale of the urban rail transit network (URTN) is one of the key tasks of URTN planning. The scale should match the urban development (UD). A reasonable scale can improve travel efficiency, increase economic activities, and promote UD, while an unreasonable scale may consume more urban resources, fail to meet urban transportation demands, and even inhibit UD. Currently, the URTN scale is primarily determined by qualitative analyses and static indicators, which leads to the scale does not match UD perfectly. To determine a reasonable scale, a System Dynamics–Lotka–Volterra (SD-LV) model is constructed. The SD model is adopted to simulate the dynamic interaction between the URT and UD. The LV (Lotka–Volterra) model is employed to calculate the scale, in which the mutualism coefficients are proposed to characterize the mutualistic relationships between the URT and UD. The model is validated by using a dataset of the Beijing URTN from 2017 to 2021. The simulation errors of the URTN scale range from −4.3% to 1.32%, which demonstrates the robustness and effectiveness of the proposed model. The study offers quantitative theoretical insights for determining the reasonable scale of the URTN.

Alternative cliques of coexisting species in complex ecosystems

The possibility that some ecosystems can exist in alternative stable states has profound implications for ecosystem conservation and restoration. Current ecological theory on multistability mostly relies on few-species dynamical models, in which alternative states are intrinsically related to specific non-linear dynamics. Recent theoretical advances, however, have shown that multiple stable ‘cliques’—small subsets of coexisting species—can be present in species-rich models even under linear interactions. Yet, the mechanisms governing the appearence and characteristics of these cliques remain largely unexplored. In the present work, we investigate cliques in the generalized Lotka–Volterra model with mathematical and computational techniques. Our findings reveal that simple probabilistic and dynamical constraints can explain the appearence, properties and stability of cliques. Our work contributes to the understanding of alternative stable states in complex ecological communities.

ROVA: A Practical, Parsimonious Volterra Model for Modulated Microwave Systems

ROVA: A Practical, Parsimonious Volterra Model for Modulated Microwave Systems

Highly controllable stabilization and switching of multiple colliding soliton sequences with generic Ginzburg–Landau gain–loss

We investigate propagation of J soliton sequences in a nonlinear optical waveguide array with generic weak Ginzburg–Landau (GL) gain–loss and nearest-neighbor (NN) interaction. The propagation is described by a system of J perturbed coupled nonlinear Schrödinger (NLS) equations. The NN interaction property leads to the elimination of collisional three-pulse interaction effects, which prevented the observation of stable multisequence soliton propagation with J>2 sequences in the presence of generic GL gain–loss in all previous studies. We show that the dynamics of soliton amplitudes can be described by a generalized J-dimensional Lotka–Volterra (LV) model. Stability and bifurcation analysis for the equilibrium points of the LV model, which is augmented by an application of the Lyapunov function method, is used to develop setups that lead to robust and scalable transmission stabilization and switching for a general J value. The predictions of the LV model are confirmed by extensive numerical simulations with the perturbed coupled-NLS model with J=3, 4, and 5 soliton sequences. Furthermore, soliton stability and the agreement between the LV model’s predictions and the simulations are not reduced with increasing value of J. Therefore, our study provides the first demonstration of robust control of multiple colliding sequences of NLS solitons in the presence of generic weak GL gain–loss with an arbitrary number of sequences. Due to the robustness and scalability of the results, they can have important applications in stabilization and switching of broadband soliton-based optical waveguide transmission.

Inverse design of the radiation temperature for indirect laser-driven equation-of-state measurement

The theoretical design for the time profile of radiation temperature plays an important role in indirect laser-driven equation-of-state measurement, which severely relies on a large number of radiation hydrodynamic simulations. In this work, we provide a concise data-driven method for optimizing the radiation temperature profile, which combines a time-varying Volterra model with an improvement achieved by data generation via radiation hydrodynamic simulations utilizing random perturbations in a skew normal distribution as inputs. We find that the time-varying Volterra model can be used to investigate the time-dependent relationship between the radiation temperature and the key physical quantities of interest, such as shock-wave velocity and ablation drive pressure. With this method, we realize the inverse designs of the radiation temperature profiles for planar dynamic shock and ramp compressions according to the desired shock-wave velocity and drive pressure, respectively, which shows the advantage of practical application in experiments.

Stability and co-existence state traveling wave solution for a general N-dimensional diffusive delayed Lotka-Volterra equation in a cylinder

Abstract A general $N$-dimensional non-monotone delayed diffusive Lotka–Volterra model is considered in our paper. First, we obtain the global stability of the model subject to Neumann boundary condition by using a small delay result for delayed systems. Second, the limits at $+\infty $ of bounded travelling wave solutions are confirmed by virtue of such global stability. Therefore, the existence of co-existence state travelling wave solutions is established. Finally, an example is given to illustrate the biological significance of the assumptions in the current paper.