Optimal harvesting policy of a stochastic predator–prey model with time delay

This paper concerns the optimal harvesting of a stochastic delay predator–prey model. Sufficient and necessary conditions for the existence of an optimal control are established. The optimal harvesting effort and the maximum value of the cost function are obtained as well. Some numerical tests are given to illustrate the main results.     

Stochastic delay foraging arena predator–prey system with Markov switching

Abstract

In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to find out how the interactions between white noise, telegraph noise and time delay affect the dynamics of the population system. Firstly, the existence of a global positive solution is verified. Then the long-time properties including the stochastically ultimate boundedness, extinction and some other asymptotic pathwise estimation of this population system are studied. Finally, the main results are illustrated by two examples.     

Robust cycles in Kolmogorov–Lotka–Volterra class of models with intraspecific co-operation

Using the Andronov–Hopf bifurcation theorem and the Poincaré–Bendixson Theorem, we explore robust cyclical possibilities in Kolmogorov–Lotka–Volterra class of models with positive intraspecific cooperation (in the form of social networks) in the prey population. We find that this additional feedback effect of intraspecific cooperation introduces nonlinearities which modify the cyclical outcomes of the model. We show that the cyclical outcomes are more robust than in the existing literature in this area due to introduction of such non-linearities. We also demonstrate the possibilities of multiple limit cycles under certain situations.     

Adaptive control of nonlinear complex Holling II predator–prey system with unknown parameters

In recent years, control of nonlinear complex predator–prey systems has attracted the attention of many researchers. The previous works have some weaknesses such as neglecting the consideration of the effects of both model uncertainties and unknown parameters and having an infinite time of convergence. To overcome the mentioned shortages, this article solves the problem of robust control of nonlinear complex Holling type II predator–prey system in a given finite time. It is assumed that the parameters of the system are fully unknown in advance and some uncertainties perturb the system's dynamics. To tackle the system unknown parameters, some adaptation laws are introduced. Thereafter, a robust switching controller is proposed to finite‐timely stabilize the predator–prey system. An illustrative example demonstrates the efficiency and usefulness of the proposed control strategy. © 2015 Wiley Periodicals, Inc. Complexity 21: 260–266, 2016     

Stability and Hopf bifurcation of a diffusive predator‐prey model with hyperbolic mortality

The dynamics of a reaction‐diffusion predator‐prey model with hyperbolic mortality and Holling type II response effect is considered. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. We also study the spatially homogeneous and nonhomogeneous periodic solutions through all parameters of the system which are spatially homogeneous. To verify our theoretical results, some numerical simulations are also presented. © 2015 Wiley Periodicals, Inc. Complexity 21: 34–43, 2016     

两类两种群动力学方程的稳定性分析

本文研究两种群动力学方程平衡点的稳定性.讨论两个捕食者-食饵-领地模型,模型用1微分方程描述,模型2用积分微分方程描述.得出平衡点稳定的条件.所得结果指出可实现总体的种群稳定而不管局部的绝灭.     

MULTISPECIES AND SINGLE‐SPECIES MODELS OF FISH POPULATION DYNAMICS: COMPARING PARAMETER ESTIMATES

Abstract Population features inferred from single‐species, age‐structured models are compared to those inferred from a multispecies, age‐structured model that includes predator‐prey interactions among three commercially harvested fish species—walleye pollock, Atka mackerel, and Pacific cod—on the Aleutian Shelf, Alaska. The multispecies framework treats the single‐species models and data as a special case of the multispecies model and data. The same data from fisheries and surveys are used to estimate model parameters for both single‐species and multispecies configurations of the model. Additionally, data from stomach samples and predator rations are used to estimate the parameters of the multispecies model. One form of the feeding functional response, predator pre‐emption, was selected using AIC from seven alternative models for how the predation rate changes with the densities of prey and possibly other predators. Differences in estimated population dynamics and productivity between the multispecies and single‐species models were observed. The multispecies model estimated lower mackerel population sizes from 1964–2003 than the single‐species model, while the spawning biomass of pollock was estimated to have declined more than three times faster since 1964 by the multispecies model. The variances around the estimates of spawning biomass were smaller for mackerel and larger for pollock in the multispecies model compared to the single‐species model.     

具有脉冲效应和功能反应的捕食系统的周期解

研究具有时滞、Holling-类功能反应和脉冲效应的捕食-食饵系统正周期解的存在性.利用Mawhin重合度理论和同伦性质,获得周期解存在的充分条件.结果推广和改进一些最近文献结论.     

一类Lotka—Volterra型捕食与被捕食系统的Flip分岔

本文利用中心流形定理和映射的分岔理论,研究了一类离散的捕食与被捕食系统的Flip分岔的存在性与稳定性,并给出了数值模拟的结果。     

Bifurcation of periodic solution in a Predator–Prey type of systems with non-monotonic response function and periodic perturbation

A Predator–Prey type of dynamical systems with non-monotonic response function and time-periodic perturbation is considered in this paper. We present a proof for the number of equilibria in the unperturbed system at some parts of the parameter space. The perturbed system is a dynamical system defined by a periodic vector field. We present an alternative proof for a classical result on the period of the periodic solution. By using a numerical continuation method AUTO (Doedel et al., 1986 [9]), we present a bifurcation analysis for periodic solution of the perturbed system where we found fold, cusp and Swallowtail bifurcations.