A prey–predator model with refuge for prey and additional food for predator in a fluctuating environment

Das, Amartya; Samanta, G. P.

doi:10.1016/j.physa.2019.122844

Cited by 51 publications

(12 citation statements)

References 26 publications

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“…In addition, based on our results, from the perspective of ecological protection, we can provide additional food to the predators to ensure that the prey population and predator population maintain a high-density level. On the one hand, it can reduce the predation rate of the predator population to the prey [30]; on the other hand, it can ensure that the predator population will not be completely extinct when the refuge rate of the prey population is high.…”

Section: Discussionmentioning

confidence: 99%

“…For example, crabs on the beach hide under sand or stones to avoid seabirds, thus increasing their survival chance. In recent years, different predator-prey systems with refuges have attracted much attention [6,[27][28][29][30]. In [27], Qi and Meng studied the threshold behavior of a stochastic predator-prey system with prey refuge and fear effect.…”

Section: Introductionmentioning

confidence: 99%

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A Stochastic Holling-Type II Predator-Prey Model with Stage Structure and Refuge for Prey

Shi

Huang

Wei

et al. 2021

Advances in Mathematical Physics

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In this paper, we study a stochastic Holling-type II predator-prey model with stage structure and refuge for prey. Firstly, the existence and uniqueness of the global positive solution of the system are proved. Secondly, the stochastically ultimate boundedness of the solution is discussed. Next, sufficient conditions for the existence and uniqueness of ergodic stationary distribution of the positive solution are established by constructing a suitable stochastic Lyapunov function. Then, sufficient conditions for the extinction of predator population in two cases and that of prey population in one case are obtained. Finally, some numerical simulations are presented to verify our results.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Stochastic Holling-Type II Predator-Prey Model with Stage Structure and Refuge for Prey

Shi

Huang

Wei

et al. 2021

Advances in Mathematical Physics

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“…The notion of extinction is one of the key subjects in population dynamics. In biological terms the extinction occurs in a population if there is no individual that can reproduce or create a new generation in a long term [12]. In mathematical terms a population goes to extinction with probability one if lim t→∞ X (t) = 0, where X is the density of a population.…”

Section: Extinction Probabilitymentioning

confidence: 99%

Exploring a Simple Stochastic Mathematical Model Including Fear with a Linear Functional Response

Gökçe

2021

Fundamental Journal of Mathematics and Applications

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This paper concentrates on a simple population model incorporating fear. Firstly, positivity and steady state analysis are performed, where the theoretical investigations show that change in the level of fear in prey population does not effect the local stability of the system around each equilibria (either stable or unstable). For the deterministic model, the numerical simulations are plotted for the density of prey species as a function of various system parameters. The stability analysis of the coexisting state shows that only transcritical bifurcation, where the steady states intersect, is observed. Secondly, the model is analysed with Gaussian noise term incorporated in the prey's death rate. The model comprising noise term turns the system into stochastic differential equations and irregular noise related oscillations are observed in the densities of both species.

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“…Ecology takes biology from the relative simplicity of individuals to explain the complexity of interactions between organisms and their environments [8,29]. Its significant implications stretch beyond biology into environmental science and the grand challenges facing society [33].…”

Section: Introductionmentioning

confidence: 99%

Stochastic bifurcations and tipping phenomena of insect outbreak systems driven by α-stable Lévy processes

Yuan¹,

Li²,

Zeng³

2022

Math. Model. Nat. Phenom.

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In this work, we mainly characterize stochastic bifurcations and tipping phenomena of insect outbreak dynamical systems driven by $\alpha$-stable L\'evy processes. In one-dimensional insect outbreak model, we find the fixed points representing refuge and outbreak from the bifurcation curves, and carry out a sensitivity analysis with respect to small changes in the model parameters, the stability index and the noise intensity. We perform the numerical simulations of dynamical trajectories using Monte Carlo methods, which contribute to looking at stochastic hysteresis phenomenon. As for two-dimensional insect outbreak system, we identify the global stability properties of fixed points and express the probability density function by the stationary solution of the nonlocal Fokker-Planck equation. Through numerical modelling, the phase portrait makes it possible to detect critical transitions among the stable states. It is then worth describing stochastic bifurcation associated with tipping points induced by noise through a careful examination of the dynamical paths of the insect outbreak system with external forcing. The results give new insight into the sensitivity of ecosystems to realistic environmental changes represented by stochastic perturbations.

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A prey–predator model with refuge for prey and additional food for predator in a fluctuating environment

Cited by 51 publications

References 26 publications

A Stochastic Holling-Type II Predator-Prey Model with Stage Structure and Refuge for Prey

A Stochastic Holling-Type II Predator-Prey Model with Stage Structure and Refuge for Prey

Exploring a Simple Stochastic Mathematical Model Including Fear with a Linear Functional Response

Stochastic bifurcations and tipping phenomena of insect outbreak systems driven by α-stable Lévy processes

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