Population Dynamics Of System Research Articles

RETRACTED ARTICLE: Model based on PDP System to simulate the forced displacement phenomenon in the Pacific Alliance

This article has been retracted from publication in the Taylor & Francis journal, Acta Agriculturae Scandinavica, Section B — Soil & Plant Science. Following publication, concerns were raised by multiple third-parties around the content of the special issue and the decision-making process. Following an investigation by the Taylor & Francis Publishing Ethics & Integrity team in full cooperation with the Editor-in-Chief, it was confirmed that this article included in Special Issue titled “ Envisage Computer Modelling and Statistics for Agriculture”, guest edited by Gunasekaran Manogaran was not peer-reviewed appropriately, in line with the Journal's peer review standards and policy. As the stringency of the peer review process is core to the integrity of the publication process, the Editor and Publisher have decided to retract all of the articles within the above-named Special Issue. The journal has not confirmed if the authors were aware of this compromised peer review process. The journal is committed to correcting the scientific record and will fully cooperate with any institutional investigations into this matter. The authors have been informed of this decision. We have been informed in our decision-making by our policy on publishing ethics and integrity and the COPE guidelines.

Determination of functional parameters in boundary conditions of linear hyperbolic systems by optimal control methods

An inverse problem of a functional parameter determination is considered for a hybrid system of population dynamics. Dynamics of several interacting populations is described by a system of first-order linear hyperbolic equations. The boundary conditions for this system are determined from the initial problem for ordinary differential equations. The problem is interpreted as an optimal control problem. A non-classic optimality condition of variational maximum principle type is proved. The original problem in distributed parameter systems is reduced to the optimal control problem for ordinary differential equations.

An Efficient Numerical Method for the Solution of the Polio Virus (Poliomyelitis) Epidemic Model with the Role of Vaccination

Mathematical modeling of a communicable disease is an effective way to describe the behavior and dynamics of the disease. It builds on our understanding of the transmission of a contagion in a population. In this paper, we explore the transmission dynamics of the polio virus (poliomyelitis) with vaccination using standard methods. We formulate an unconditionally stable Non-Standard Finite Difference (NSFD) scheme for a continuous system of the epidemic polio virus. The designed scheme to approximate the solution is bounded, consistent with the underlying model. The proposed numerical scheme preserves the positivity of the stated variables which is necessary for any population dynamical system. It is used to calculate the numerical solutions of the epidemic model for different step sizes “h”. Two other numerical schemes are enforced to find the solution of the proposed system. Finally, the comparison of the NSFD technique with these methods proves its validity and effectiveness.

A study on fractional host–parasitoid population dynamical model to describe insect species

AbstractThe parasitoid is a broad evolutionary association of hymenopteran insects which are well‐known as biological control agents. Parasites are different from predators because parasites only take resources from one host, whereas predators eat many preys. The preeminent target of this study is to present a fractional model of host–parasitoid population dynamical system through the Caputo operator. The host–parasitoid population dynamical model is a system of three dimensional coupled differential equations. This research also investigates the possibility for obtaining new chaotic behaviors with singular fractional operator and shows the chaotic behavior at different values of fractional order. Furthermore, two numerical schemes Adam–Bashforth–Moulton and new Toufik–Atangana mechanism were suggested to solve fractional host–parasitoid population numerically. Again, some numerical simulations are perform to assess the efficiency of the newly proposed method. Some attractive illustration is presented through graphically. We strongly believe that the proposed work will open various new doors of investigations toward modeling on parasitoid.

Delay-driven instability and ecological control in a food-limited population networked system

The delay and network are incorporated to describe the spatiotemporal behavior of a food-limited population dynamical system. By using the standard approach of upper and lower solutions, we have shown the global existence and uniqueness of solutions to the system. By analyzing eigenvalue spectrum, we show that the delay can cause the long-term behavior of the system from stability to instability, that is, the positive equilibrium is asymptotically stable in the absence of delay, but loses its stability such that the Hopf bifurcation occurs when the time delay increases beyond a threshold. By the norm form and the center manifold theory, we study the stability and direction of the Hopf bifurcation. We propose some formulas to control the stability and period of the bifurcating periodic solutions. Moreover, numerical simulations reveal that the network structure can switch the type of spatiotemporal patterns.

Atangana-Baleanu fractional framework of reproducing kernel technique in solving fractional population dynamics system

Abstract In this article, a class of population growth model, the fractional nonlinear logistic system, is studied analytically and numerically. This model is investigated by means of Atangana-Baleanu fractional derivative with a non-local smooth kernel in Sobolev space. Existence and uniqueness theorem for the fractional logistic equation is provided based on the fixed-point theory. In this orientation, two numerical techniques are implemented to obtain the approximate solutions; the reproducing-kernel algorithm is based on the Schmidt orthogonalization process to construct a complete normal basis, while the successive substitution algorithm is based on an appropriate iterative scheme. Convergence analysis associated with the suggested approaches is provided to demonstrate the applicability theoretically. The impact of the fractional derivative on population growth is discussed by a class of nonlinear logistical models using the derivatives of Caputo, Caputo-Fabrizio, and Atangana-Baleanu. Using specific examples, numerical simulations are presented in tables and graphs to show the effect of the fractional operator on the population curve as . The present results confirm the theoretical predictions and depict that the suggested schemes are highly convenient, quite effective and practically simplify computational time.

Steering eco-evolutionary game dynamics with manifold control.

Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature and have shown profound effects on the resulting eco-evolutionary dynamics. By incorporating linear environmental feedback law into the replicator dynamics of two-player games, recent theoretical studies have shed light on understanding the oscillating dynamics of the social dilemma. However, the detailed effects of more general nonlinear feedback loops in multi-player games, which are more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by a nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centred on cooperators not only accelerates the convergence of stable manifolds but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population state. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments.

Three-Way Interactions in an Artificial Community of Bacterial Strains Directly Isolated From the Environment and Their Effect on the System Population Dynamics.

This work is motivated by previous studies that have analyzed the population ecology of a collection of culturable thermoresistant bacteria, isolated from the Churince lagoon in Cuatro Cienegas, Mexico. In particular, it is aimed at testing a hypothesis from a modeling study, which states that antagonistic and sensitive bacteria co-exist thanks to resistant bacteria that protect sensitive ones by forming physical barriers. We selected three different bacterial strains from the referred collection: one antagonistic, one sensitive, and one resistant, and studied the population dynamics of mixed colonies. Our results show that, although the proposed protective mechanism does not work in this case, the resistant strain confers some kind of protection to sensitive bacteria. Further modeling and experimental results suggest that the presence of resistant bacteria indirectly improves the probability that patches of sensitive bacteria grow in a mixed colony. More precisely, our results suggest that by making antagonistic bacteria produce and secrete an antagonistic substance (with the concomitant metabolic cost and growth rate reduction), resistant bacteria increase the likelihood that sensitive bacteria locally outcompete antagonistic ones.

An Efficient Approach for Solving Fractional Dynamics of a Predator-Prey System

In this work, we execute a generally new analytical technique, the modified generalized Mittag-Leffler function method (MGMLFM) for solving nonlinear partial differential equations containing fractional derivative emerging in predator-prey biological population dynamics system. This dynamics system are given by a set of fractional differential equations in the Caputo sense. A new solution is constructed in a power series. The stability of equilibrium points is studied. Moreover, numerical solutions for different cases are given and the methodology is displayed. We conducted a comparing between the results obtained by our method with the results obtained by other methods to illustrate the reliability and effectiveness of our main results.

On the null controllability of the Lotka-Mckendrick system

In this work, we study null-controllability of the Lotka-McKendrick system of population dynamics. The control is acting on the individuals in a given age range. The main novelty we bring in this work is that the age interval in which the control is active does not necessarily contain a neighbourhood of $ 0. $ The main result asserts the whole population can be steered into zero in large time. The proof is based on final-state observability estimates of the adjoint system with the use of characteristics.

Numerical study for fractional model of non-linear predator-prey biological population dynamical system

The key objective of the present paper is to propose a numerical scheme based on the homotopy analysis transform technique to analyze a time-fractional non-linear predator-prey population model. The population model are coupled fractional order non-linear PDE often employed to narrate the dynamics of biological systems in which two species interact, first is a predator and the second is a prey. The proposed scheme provides the series solution with a great freedom and flexibility by choosing appropriate parameters. The convergence of the results is free from small or large parameters. Three examples are discussed to demonstrate the correctness and efficiency of the used computational approach.

Sustainable Harvesting Policies Under Long-Run Average Criteria: Near Optimality

This paper develops near-optimal sustainable harvesting strategies for the predator in a predator-prey system. The objective function is of long-run average per unit time type in the path-wise sense. To date, ecological systems under environmental noise are usually modeled as stochastic differential equations driven by a Brownian motion. Recognizing that the formulation using a Brownian motion is only an idealization, in this paper, it is assumed that the environment is subject to disturbances characterized by a jump process with rapid jump rates. Under broad conditions, it is shown that the systems under consideration can be approximated by a controlled diffusion system. Based on the limit diffusion system, control policies of the original systems are constructed. Such an approach enables us to develop sustainable harvesting policies leading to near optimality. To treat the underlying problems, one of the main difficulties is due to the long-run average objective function. This in turn, requires the handling of a number of issues related to ergodicity. New approaches are developed to obtain the tightness of the underlying processes based on the population dynamic systems.

A Biological Model for Resource Allocation and User Dynamics in Virtualized HetNet

Virtualization technology is considered an effective measure to enhance resource utilization and interference management via radio resource abstraction in heterogeneous networks (HetNet). The critical challenge in wireless virtualization is virtual resource allocation on which substantial works have been done. However, most existing researches on virtual resource allocation focus on improving total utility. Different from the existing works, we investigate the dynamic‐aware virtual radio resource allocation in virtualization based HetNet considering utility and fairness. A virtual radio resource management framework is proposed, where the radio resources of different physical networks are virtualized into a virtual resource pool and mobile virtual network operators (MVNOs) compete for virtual resources from the pool to provide service to users. A virtual radio resource allocation algorithm based on biological model is developed, considering system utility, fairness, and dynamics. Simulation results are provided to verify that the proposed virtual resource allocation algorithm not only converges within a few iterations, but also achieves a better trade‐off between total utility and fairness than existing algorithm. Besides, it can also be utilized to analyze the population dynamics of system.

Boundary effects on population dynamics in stochastic lattice Lotka–Volterra models

We investigate spatially inhomogeneous versions of the stochastic Lotka–Volterra model for predator–prey competition and coexistence by means of Monte Carlo simulations on a two-dimensional lattice with periodic boundary conditions. To study boundary effects for this paradigmatic population dynamics system, we employ a simulation domain split into two patches: Upon setting the predation rates at two distinct values, one half of the system resides in an absorbing state where only the prey survives, while the other half attains a stable coexistence state wherein both species remain active. At the domain boundary, we observe a marked enhancement of the predator population density. The predator correlation length displays a minimum at the boundary, before reaching its asymptotic constant value deep in the active region. The frequency of the population oscillations appears only very weakly affected by the existence of two distinct domains, in contrast to their attenuation rate, which assumes its largest value there. We also observe that boundary effects become less prominent as the system is successively divided into subdomains in a checkerboard pattern, with two different reaction rates assigned to neighboring patches. When the domain size becomes reduced to the scale of the correlation length, the mean population densities attain values that are very similar to those in a disordered system with randomly assigned reaction rates drawn from a bimodal distribution.

A class of epidemic virus transmission population dynamic system

A class of epidemic virus transmission population dynamic system is considered. Firstly, using the functional homotopic analysis method, an initial approximate function is selected. Then, the arbitrary order approximate analytic solutions are obtained successively. Finally, the accuracy of the obtained approximate analytic solutions is described. The influence of the various physical parameters for the epidemic virus transmission population dynamic system is discussed.

Identification of Source Terms in a Coupled Age-structured Population Model with Discontinuous Diffusion Coefficients

This article concerns the inverse problem of the coupled age-structured population dynamics system with discontinuous diffusion coefficients. The internal observations with two measurements are allowed to obtain the stability result for the inverse problem consisting of simultaneously retrieving two space dependent source terms in the given parabolic system. The proof of the result relies on Carleman estimates and certain energy estimates for parabolic system.

Co-existence of periodic bursts and death of cycles in a population dynamics system.

We study the dynamics of a discrete-time tritrophic model which mimics the observed periodicity in the population cycles of the larch budmoth insect which causes widespread defoliation of larch forests at high altitudes periodically. Our model employs q-deformation of numbers to model the system comprising the budmoth, one or more parasitoid species, and larch trees. Incorporating climate parameters, we introduce additional parasitoid species and show that their introduction increases the periodicity of the budmoth cycles as observed experimentally. The presence of these additional species also produces other interesting dynamical effects such as periodic bursting and oscillation quenching via oscillation death, amplitude death, and partial oscillation death which are also seen in nature. We suggest that introducing additional parasitoid species provides an alternative explanation for the collapse of the nine year budmoth outbreak cycles observed in the Swiss Alps after 1981. A detailed exploration of the parameter space of the system is performed with movies of bifurcation diagrams which enable variation of two parameters at a time. Limit cycles emerge through a Neimark-Sacker bifurcation with respect to all parameters in all the five and higher dimensional models we have studied.

Almost periodic solution for a population dynamic system on time scales with an application

This paper is concerned with an almost population dynamic system on time scales. Using the theory of calculus on time scales and some mathematical methods, several comparison theorems on time scales are established. Based on these results, we derive some sufficient conditions for permanence of the system. Moreover, using the properties of almost periodic functions and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of uniformly, asymptotically stable almost periodic solution of the system are obtained. As an application, we applying the obtained results to a single-species system with distributed delay on time scales. Finally, two examples together with their numerical simulations are presented to illustrate the feasibility and effectiveness of the results.

Almost periodic solution for a population dynamic system on time scales with an application

Almost periodic solution for a population dynamic system on time scales with an application

The role of East Asian monsoon system in shaping population divergence and dynamics of a constructive desert shrub Reaumuria soongarica.

Both of the uplift of Qinghai-Tibet Plateau (QTP) and the development of East Asian monsoon system (EAMS) could have comprehensively impacted the formation and evolution of Arid Central Asia (ACA). To understand how desert plants endemic to ACA responded to these two factors, we profiled the historical population dynamics and distribution range shift of a constructive desert shrub Reaumuria soongarica (Tamaricaceae) based on species wide investigation of sequence variation of chloroplast DNA and nuclear ribosomal ITS. Phylogenetic analysis uncovered a deep divergence occurring at ca. 2.96 Mya between the western and eastern lineages of R. soongarica, and ecological niche modeling analysis strongly supported that the monsoonal climate could have fragmented its habitats in both glacial and interglacial periods and impelled its intraspecific divergence. Additionally, the population from the east monsoonal zone expanded rapidly, suggesting that the local monsoonal climate significantly impacted its population dynamics. The isolation by distance tests supported strong maternal gene flow along the direction of the East Asian winter monsoon, whose intensification induced the genetic admixture along the latitudinal populations of R. soongarica. Our results presented a new case that the development of EAMS had prominently impacted the intraspecific divergence and population dynamics of this desert plant.