Population Dynamics Of System Research Articles

Hierarchical Stackelberg Control for a Two-Stroke Linear System in Population Dynamics

We study a unique hierarchical control problem for a two-stoke linear system, adjoint to an age and space dependent population dynamics problem. Using Stackelberg's method, we introduce two levels of control: a boundary control to achieve optimal flow regulation and a distributed control for null controllability. Our approach employs Carleman inequalities to address non-homogeneous Dirichlet boundary conditions, leading to new insights in controlling invasive species populations. These results highlight the applicability of hierarchical controls in ecological systems, providing a robust framework for future studies in control theory and population dynamics.

Intelligent optimal control of nonlinear diabetic population dynamics system using a genetic algorithm

Diabetes is a chronic disease affecting millions of people worldwide. Several studies have been carried out to control the diabetes problem, involving both linear and non-linear models. However, the complexity of linear models makes it impossible to describe the diabetic population dynamic in depth. To capture more detail about this dynamic, non-linear terms were introduced into the mathematical models, resulting in more complicated models strongly consistent with reality (capable of re-producing observable data). The most commonly used methods for control estimation are Pantryagain’s maximum principle and Gumel’s numerical method. However, these methods lead to a costly strategy regarding material and human resources; in addition, diabetologists cannot use the formulas implemented by the proposed controls. In this paper, the authors propose a straightforward and well-performing strategy based on non-linear models and genetic algorithms (GA) that consists of three steps: 1) discretization of the considered non-linear model using classical numerical methods (trapezoidal rule and Euler–Cauchy algorithm); 2) estimation of the optimal control, in several points, based on GA with appropriate fitness function and suitable genetic operators (mutation, crossover, and selection); 3) construction of the optimal control using an interpolation model (splines). The results show that the use of the GA for non-linear models was successfully solved, resulting in a control approach that shows a significant decrease in the number of diabetes cases and diabetics with complications. Remarkably, this result is achieved using less than 70% of available resources.

Theoretical exploration and controller design of bifurcation in a plankton population dynamical system accompanying delay

Theoretical exploration and controller design of bifurcation in a plankton population dynamical system accompanying delay

Periodic solution analysis of a population dynamics system model for pulsating organisms

Abstract Population dynamics has a wide range of applications in ecological theory, especially in the fields of plant and animal conservation and the management and development of ecological environments. Periodic solution analysis of a population dynamics model for pulsating organisms. The influence of impulsive dynamics on the periodic solution of the system is investigated in this paper, which considers several types of population dynamics systems with impulsive effects. First, the impulsive differential modeling of the model of a constantator in a polluted environment considering time-lagged growth response and impulsive inputs proves that only ̄t needs to be sufficiently large to have x(t) > m x, such that, the constantator seeks a unique periodic solution for microbial extinction and persistent survivability. Next, a model of integrated pest control is modeled to find, a periodic solution for pest extinction and the existence of (0, I* (t)) is globally stable. Then, a Lur’e system with impulsive biodynamics is explored, modeled with uncertain parameters, and simulated with Chua’s circuit system to determine that the state trajectory lines all eventually converge to 0 and have stable periodic solutions. Finally, the Beddington-DeAngelis predator-prey model with impulsive effects is used to argue, using correlation priming, for the existence of z i * ( t ) = exp { x i * ( t ) } z_i^*\left( t \right) = \exp \left\{ {x_i^*\left( t \right)} \right\} , i = 1, 2, such that z * ( t ) = ( z 1 * ( t ) , z 2 * ( t ) ) T {z^*}\left( t \right) = {\left( {z_1^*\left( t \right),\,z_2^*\left( t \right)} \right)^T} there is a positive ω − periodic solution for this system.

Uncertain Stochastic Hybrid Age-Dependent Population Equation Based on Subadditive Measure: Existence, Uniqueness and Exponential Stability

The existing literature lacks a study on age-dependent population equations based on subadditive measures. In this paper, we propose a hybrid age-dependent population dynamic system (referred to as APDS) that incorporates uncertain random perturbations driven by both the well-known Wiener process and the Liu process associated with belief degree, which have similar symmetry in terms of form. Firstly, we redefine the Liu integral in a mean square sense and then extend Liu’s lemma and the Itô-Liu formula. We then utilize the extensions of the Itô-Liu formula, Barkholder-Davis-Gundy (BDG) inequality, the Liu’s lemma, the Gronwall’s lemma and the symmetric nature of calculus itself to establish the uniqueness of a strong solution for the hybrid APDS. Additionally, we prove the existence of the hybrid APDS by combining the proof of uniqueness with some important lemmas. Finally, under appropriate assumptions, we demonstrate the exponential stability of the hybrid system.

<span>Changing perception through the art of mathematical modeling</span>

Nowadays, infectious diseases are disorders caused by organisms — such as bacteria, viruses, fungi or parasites. Many organisms live in and on our bodies. They’re normally harmless or even helpful. But certain microbes have the potential to cause disease in specific situations. It is possible for some infectious diseases to spread from person to person. Others are spread by animals or insects. In this study, we build certain fundamental models, such as SI, SIR, SIRS, and SEIR, and in numerical simulations, we take into account random parameters to determine the dynamics of the model’s behavior. Finally, we present several studies in mathematical modeling of real situation relevant to epidemiology and population dynamic systems.

Fear and Group Defense Effect of a Holling Type IV Predator-Prey System Intraspecific Competition

Field and experimental data on aquatic ecosystem species show the effect of fear on changing prey demographics. The fear effect has an impact on aquatic ecosystems, such as species migration to settled areas. In this paper, the type of research described is a literature study. The cost effect assigned to the reproductive system of the prey population and the predation function response are given as Holling Type IV for research purposes to model the fear effect. Some research novelties, the equilibrium points are all shown in the population dynamics system model with an analysis of positive equilibrium. Positive and biologically realistic equilibrium points were analyzed using the Routh-Hurwitz criterion which is mathematically a local asymptotically stable. A pair of imaginary eigenvalues with a negative real part can increase population growth. An equilibrium region showing equilibrium for several parameters such as extinction, no predators, and two populations coexisting in a sustainable manner. The correlation and fluctuation of fear and fear cost were investigated to obtain a better model. The results of the numerical simulations show that the prey population becomes more daring to fight or fighting power with significant prey growth rates or high predator mortality rates. Doi: 10.28991/ESJ-2023-07-02-06 Full Text: PDF

Analysis of a Modified System of Infectious Disease in a Closed and Convex Subset of a Function Space with Numerical Study

In this article, the transmission dynamical model of the deadly infectious disease named Ebola is investigated. This disease identified in the Democratic Republic of Congo (DRC) and Sudan (now South Sudan) and was identified in 1976. The novelty of the model under discussion is the inclusion of advection and diffusion in each compartmental equation. The addition of these two terms makes the model more general. Similar to a simple population dynamic system, the prescribed model also has two equilibrium points and an important threshold, known as the basic reproductive number. The current work comprises the existence and uniqueness of the solution, the numerical analysis of the model, and finally, the graphical simulations. In the section on the existence and uniqueness of the solutions, the optimal existence is assessed in a closed and convex subset of function space. For the numerical study, a nonstandard finite difference (NSFD) scheme is adopted to approximate the solution of the continuous mathematical model. The main reason for the adoption of this technique is delineated in the form of the positivity of the state variables, which is necessary for any population model. The positivity of the applied scheme is verified by the concept of M-matrices. Since the numerical method gives a discrete system of difference equations corresponding to a continuous system, some other relevant properties are also needed to describe it. In this respect, the consistency and stability of the designed technique are corroborated by using Taylor’s series expansion and Von Neumann’s stability criteria, respectively. To authenticate the proposed NSFD method, two other illustrious techniques are applied for the sake of comparison. In the end, numerical simulations are also performed that show the efficiency of the prescribed technique, while the existing techniques fail to do so.

The effect of Lévy noise and white noise on a Leslie-Gower predator-prey system with prey refuge

A stochastic Leslie-Gower predator-prey system with prey refuge is discussed, L$ \acute{e} $vy noise and white noise are adopted to simulate the random change of environment. The existence of global positive solution and the stochastic boundedness is proved, the threshold conditions of extinction and stable in the mean are given, the long time behavior of solution for the predator-prey system is also considered. In the end, some examples of numerical simulation are given to verify these conclusions. Compared to the deterministic system, the prey population and the predator population will be extinct, when the intensity of noise is large enough, however, it does not happen in the deterministic system, where the positive equilibrium is always globally stable. These results indicate that the stochastic change of environment has great influence on the population dynamic system.

Time delays and pollution in an open‐access fishery

AbstractWe analyze the impacts of pollution on fishery sector using a dynamical system approach. The proposed model presupposes that the economic development causes emissions that either remediate or accumulate in the oceans. The model possesses a block structure where the solutions of the rate equations for the pollutant and the economic activity act as an input for the biomass and effort equation. We also account for distributed delay effects in both the pollution level and the economic activity level in our modeling framework. The weight functions in the delay terms are expressed in terms of exponentially decaying functions, which in turn enable us to convert the modeling framework to a higher‐order autonomous dynamical system by means of a linear chain trick. When both the typical delay time for the economic activity and the typical delay time for the pollution level are much smaller than the biomass time scale, the governing system is analyzed by means of the theory for singularly perturbed dynamical systems. Contrary to what is found for population dynamical systems with absolute delays, we readily find that the impact of the distributed time lags is negligible in the long‐run dynamics in this time‐scale separation regime. Recommendations for Resource Managers Resource managers should be aware of the dynamical interrelations between fisheries and pollution, also those that are time delayed. Time lags between biological, economic, and environmental variables are affecting the time paths of these variables. In the long run, the impact from distributed time lags have a negligible influence on the long‐run dynamical evolution. Neither the past history of economic activities nor the past history of pollution growth can affect the fishery dynamics in the long run. More empirical and theoretical research are needed to increase our understanding of the interrelation between fisheries and pollution.

Noise in Biomolecular Systems: Modeling, Analysis, and Control Implications

While noise is generally associated with uncertainties and often has a negative connotation in engineering, living organisms have evolved to adapt to (and even exploit) such uncertainty to ensure the survival of a species or implement certain functions that would have been difficult or even impossible otherwise. In this article, we review the role and impact of noise in systems and synthetic biology, with a particular emphasis on its role in the genetic control of biological systems, an area we refer to as cybergenetics. The main modeling paradigm is that of stochastic reaction networks, whose applicability goes beyond biology, as these networks can represent any population dynamics system, including ecological, epidemiological, and opinion dynamics networks. We review different ways to mathematically represent these systems, and we notably argue that the concept of ergodicity presents a particularly suitable way to characterize their stability. We then discuss noise-induced properties and show that noise can be both an asset and a nuisance in this setting. Finally, we discuss recent results on (stochastic) cybergenetics and explore their relationships to noise. Along the way, we detail the different technical and biological constraints that need to be respected when designing synthetic biological circuits. Finally, we discuss the concepts, problems, and solutions exposed in the article; raise criticisms and concerns about current ideas and approaches; suggest current (open) problems with potential solutions; and provide some ideas for future research directions.

Optimal Control for a Degenerate Population Model in Divergence Form With Incomplete Data

In this paper, we study the control of a degenerate population dynamics system in divergence form with unknown information on the boundary. We use the no-regret control concept of J. L. Lions treated in (Lions, 1992) to investigate the problem. At first, we define notions of no-regret control.  Using an appropriate Hilbert space, we show that the no-regret control is the limit near the origin of a series of low-regret controls defined by a quadratic perturbation previously used by (Nakoulima, Omrane, & Velin, 2000) corresponding to the disturbed system and for which we give a singular optimality system.

Weather, fire, and density drive population dynamics of small mammals in the Brazilian Cerrado

AbstractUnderstanding the relative importance of exogenous and endogenous factors in natural population dynamics has been a central question in ecology. However, until recently few studies used long-term data to assess factors driving small mammal abundance in Neotropical savannas. We used a 9-year data set, based on monthly captures, to understand the population dynamics of two scansorial small mammals inhabiting the Brazilian Cerrado: the semelparous gracile mouse opossum (Gracilinanus agilis), and the iteroparous long-tailed climbing mouse (Rhipidomys macrurus), the two most abundant species at Panga Ecological Station (Uberlândia/MG). We tested the impact of two fires that occurred in 2014 and 2017 on the abundance of both populations. Also, we used Royama’s framework to identify the role of the endogenous system (intraspecific competition) and exogenous factors (annual rainfall, days with minimum and maximum temperatures, annual minimum Normalized Difference Vegetation Index [NDVI], and Southern Oscillation Index) in population dynamics. Extensive and severe fires had a lasting, negative impact on the studied populations, probably by reducing the carrying capacity of the environment. Both populations were influenced by negative first-order feedback, indicating density-dependent effects. Moreover, the endogenous system and the annual minimum NDVI operated as vertical effects determining G. agilis dynamics, while the R. macrurus population was governed by the vertical effects of 1-year lagged rainfall. Our results support the contention that small mammal population fluctuations are driven by the interaction between endogenous (density-dependent) and exogenous factors, which in this study were mainly associated with habitat complexity. Despite ecological similarities shared by both species, their response and recovery time to disturbances and environmental variables varied, probably due to their contrasting life histories. Hence, we emphasize the need to consider species life histories to understand the responses of small mammals to extreme events and reinforce the importance of long-term studies that evaluate the combined effects of endogenous and exogenous variables on population dynamics.

Approximate controllability of the semilinear population dynamics system with diffusion

This paper aims to study the approximate controllability of semilinear population dynamics system with diffusion using semigroup theory. The semilinear population dynamical model with the nonlocal birth process is transformed into a standard abstract semilinear control system by identifying the state, control, and the corresponding function spaces. The state and control spaces are assumed to be Hilbert spaces. The semigroup theory is developed from the properties of the population operators and Laplacian operators. Then the approximate controllability results of the system are obtained using ‐semigroup approach and some other simple conditions on the nonlinear term and operators involved in the model.

Stability analysis of a predator-prey model with stage structure

Many scholars have explored the population dynamics system, functional response, time-delay response, and so on. Based on the existing research, this paper studies a class of predator-prey models with stage structure, time delay, and Holling type-II functional response function. The stability of that model at the positive equilibrium point, the sufficient condition for stability, and the existence of Hopf bifurcation are discus. The model was numerically simulated by taking appropriate parameters and different time delay values, variation diagram of each component, and solution curves were given near the critical value. The results show that the stability of the system will change with the variation of the bifurcation parameter value, and Hopf bifurcation will occur.

New discussion concerning to optimal control for semilinear population dynamics system in Hilbert spaces

The objective of our paper is to investigate the optimal control of semilinear population dynamics system with diffusion using semigroup theory. The semilinear population dynamical model with the nonlocal birth process is transformed into a standard abstract semilinear control system by identifying the state, control, and the corresponding function spaces. The state and control spaces are assumed to be Hilbert spaces. The semigroup theory is developed from the properties of the population operators and Laplacian operators. Then the optimal control results of the system are obtained using the C0-semigroup approach, fixed point theorem, and some other simple conditions on the nonlinear term as well as on operators involved in the model.

Discrete stage-structured tick population dynamical system with diapause and control.

A discrete stage-structured tick population dynamical system with diapause is studied, and spraying acaricides as the control strategy is considered in detail. We stratify vector populations in terms of their maturity status as immature and mature subgroups. The immature subgroup is divided into two categories: normal immature and diapause immature. We compute the net reproduction number $ R_0 $ and perform a qualitative analysis. When $ R_0 < 1 $, the global asymptotic stability of tick-free fixed point is well proved by the inherent projection matrix; there exists a unique coexistence fixed point and the conditions for its asymptotic stability are obtained if and only if $ R_0 > 1; $ the model has transcritical bifurcation if $ R_0 = 1. $ Moreover, we calculate the net reproduction numbers of the model with constant spraying acaricides and periodic spraying acaricides, respectively, and compare the effects of the two methods on controlling tick populations.

Bistability in a One-Dimensional Model of a Two-Predators-One-Prey Population Dynamics System

In this paper, we study the classical two-predators-one-prey model. The classical model described by a system of 3 ordinary differential equations can be reduced to a one-dimensional bimodal map. We prove that this map has at most two stable periodic orbits. Besides, we describe the structure of bifurcations of the map. Finally, we describe a mechanism that yields bistable regimes. We find several areas of bistability numerically.

Hopf Bifurcation for a FitzHugh–Nagumo Model with Time Delay in a Network

A reaction diffusion system is used to study the interaction between species in a population dynamic system. It is not only used in a population dynamic system with the diffusion phenomenon but also used in physical chemistry, medicine, and animal and plant protection. It has been studied by more and more scholars in recent years. The FitzHugh–Nagumo model is one of the most famous reaction-diffusion models. This article takes a deeper look at a FitzHugh–Nagumo model in a network with time delay. Firstly, we studied the linear stability of the equilibrium, then the existence of Hopf bifurcation is given, and finally, the stability of the Hopf bifurcation is introduced.

Model of neo-Malthusian population anticipating future changes in resources

In this paper we develop a class of models to study a population and resource dynamical system in which the decision to give birth is based on a rational far-sighted cost–benefit analysis on what the future of the resource level will be. This leads to consider a system in which a time forward population/resource dynamical system is coupled with a time backward Bellman’s equation (which models the choice of having a child). We construct, from a population model with food consumption, an example, to study the change in time of the fertility rate when a catastrophic change in resource is announced at a given moment, when a birth control policy is announced and we compare these two announcements in case nothing happens. Moreover, we provide, mathematical tools to theoretically and numerically study this complex coupling of time forward and time backward equations.