Uniform persistence of multispecies ecological competition predator-pray system with Holling Ⅲ type functional response

The main purpose of this paper is to study the persistence of the general multispecies competition predator-pray system with Holling Ⅲ type functional response. In this system, the competition among predator species and among prey species are simultaneously considered. By using the comparison theory and qualitative analysis, the sufficient conditions for uniform strong persistence are obtained.

Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters

In recent years,rumor spreading has caused widespread public panic and affected the whole social harmony and stability.Consequently,how to control the rumor spreading effectively and reduce its negative influence urgently needs people to pay much attention.In this paper,we mainly study the near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters.Firstly,the science knowledge propagation and the refutation mechanism as the control strategies are introduced into a stochastic rumor spreading model.Then,some sufficient and necessary conditions for the near-optimal control of the stochastic rumor spreading model are discussed respectively.Finally,through some numerical simulations,the validity and availability of theoretical analysis is verified.Meanwhile,it shows the significance and effectiveness of the proposed control strategies on controlling rumor spreading,and demonstrates the influence of stochastic disturbance and imprecise parameters on the process of rumor spreading.

Stability and Bifurcation Analysis of a Discrete Predator-Prey Model with Mixed Holling Interaction

In this paper,a discrete Lotka-Volterra predator-prey model is proposed that considers mixed functional responses of Holling types I and III.The equilibrium points of the model are obtained,and their stability is tested.The dynamical behavior of this model is studied according to the change of the control parameters.We find that the complex dynamical behavior extends from a stable state to chaotic attractors.Finally,the analytical results are clarified by some numerical simulations.

Positive solutions for a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-Ⅱ functional response

We consider a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-II functional response.The main concern is the existence of positive solutions under the combined effect of cross-diffusion and Holling type-II functional response.Here,a positive solution corresponds to a coexistence state of the model.Firstly,we study the sufficient conditions to ensure the existence of positive solutions by using degree theory and analyze the coexistence region in parameter plane.In addition,we present the uniqueness of positive solutions in one dimension case.Secondly,we study the stability of the trivial and semi-trivial solutions by analyzing the principal eigenvalue of the corresponding linearized system,and then we characterize the stable/unstable regions of semi-trivial solutions in parameter plane.

A Stage-Structured Predator-Prey System with Impulsive Effect and Holling Type-Ⅱ Functional Response

A stage-structured predator-prey system with impulsive effect and Holling type-II functional response is investigated. By the Floquet theory and small amplitude perturbation skills, it is proved that there exists a global stable pest-eradication periodic solution when the impulsive period is less than some critical values. Farther, the conditions for the permanence of system are established. Numerical simulations are carried out to illustrate the impulsive effect on the dynamics of the system.

Spatial pattern formation of a ratio-dependent predator-prey model

This paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatially distributed population with diffusion in a Holling-III ratio-dependent predator-prey model, the sufficient conditions for diffusion-driven instability with Neumann boundary conditions are obtained. Furthermore, it presents novel numerical evidence of time evolution of patterns controlled by diffusion in the model, and finds that the model dynamics exhibits complex pattern replication, and the pattern formation depends on the choice of the initial conditions. The ideas in this paper may provide a better understanding of the pattern formation in ecosystems.

ALMOST PERIODIC SOLUTION OF MULTISPECIES COMPETITION-PREDATOR SYSTEM WITH ROLLING'S TYPE Ⅲ FUNCTIONAL RESPONSE

In this paper, we consider a nonautonomous multispecies competition-predator system with Holling＇s type Ⅲ functional response. The coexistence of the system, under some conditions, is obtained. Furthermore, using Lyapunov function, we show that the system has a strictly positive almost periodic solution which is globally asymptotically stable.

Dynamics of a stochastic Holling II predator-prey model with Levy jumps and habitat complexity

This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique,and the stochastic ultimate boundedness of this positive solution is also obtained.Sufficient conditions are established for the extinction and persistence of this solution.Moreover,some numerical simulations are carried out to support the obtained results.

Dynamics of a delay-induced prey-predator system with interaction between immature prey and predators

In biological pest control systems,several pests(including insects,mites,weeds,etc.)are controlled by biocontrol agents that rely primarily on predation.Following this biocontrol management ecology,we have created a three-tier prey-predator model with prey phase structure and predator gestation delay.Several studies have demonstrated that predators with Holling type-II functional responses sometimes consume immature prey.A study of the well-posedness and local bifurcation(such as saddle-node and transcritical)near the trivial and planer equilibrium points is carried out.Without any time lag,the prey development coeficient has a stabilizing impact,while increasing attack rate accelerates instability.Energy transformation rate and handling time are shown to cause multiple stability switches in the system.Numerical results demonstrate time delay is the key destabilizer that destroys stability.Our model can replicate more realistic events by including time-dependent factors and exploring the dynamic behavior of nonautonomous systems.In the presence of time delay,sufficient conditions of permanence and global attractivity of the nonautonomous system are derived.Finally,MATLAB simulations are performed to validate the analytical findings.

THE EFFECTS OF TIMING OF PULSE SPRAYING AND RELEASING PERIODS ON DYNAMICS OF GENERALIZED PREDATOR-PREY MODEL

Based on the facts of releasing natural enemies and spraying pesticides at different time points, we propose a generalized predator-prey model with impulsive interventions. The threshold values for the existence and stability of pest eradication periodic solution are provided under the assumptions of releasing natural enemies either more or less frequent than spray. In order to address how the different pulse time points, control tactics affect the pest control （i.e. the threshold value）, the Holling Type II Lotka-Volterra predator- prey system, as an example, with impulsive intervention at different time points axe investigated carefully. The numerical results show how the threshold values are affected by the factors including instantaneous killing rates of pesticides on pests and natural enemies, the release rate of natural enemies and release constant, timing of pesticide application and timing of release period. Furthermore, it is confirmed that the system has the coexistences of pests and natural enemies for a wide range of parameters and with quite different pest amplitudes.

Alternative food and external source of infection stabilize predator-prey oscillations -- A conclusion drawn from an eco-epidemiological model

Das et al. [Effect of disease-selective predation on prey infected by contact and external sources, Biosystems 95（3） （2009） 188-199] proposed an eco-epidemiological model where the prey species is infected through the external source of infection and contact of the species. In this present study we have modified their model by assuming that the predator consumes both the susceptible as well as the infected prey following the modified Holling type-Ⅱ functional response. Our main focusing points of this study are the role of infection rate （both internal and external）, alternative food, and half-saturation constant in the predator prey dynamics with disease in the prey population. We have shown the local stability of the boundary as well as the interior equilibrium point under certain conditions. We have Mso worked out the permanence of the system. Our simulation results show that the system enters into limit cycle oscillations from stable position for higher values of the contact rate. But it is also shown that the external infection rate, enrichment of the alternative food of the predator population and the half-saturation constant can prevent limit cycle oscillations and stabilize the system. Thus external dis- ease propagation, enrichment of the alternative food resource, and the half-saturation constant are the key factors for preventing the oscillatory behavior of the species.

A multi-delay model for pest control with awareness induced interventions — Hopf bifurcation and optimal control analysis

Farming awareness is an important measure for pest controlling in agricultural practice.Time delay in controlling pest may affect the system.Time delay occurs in organizing awareness campaigns,also time delay may takes place in becoming aware of the control strategies or implementing suitable controlling methods informed through social media.Thus we have derived a mathematical model incorporating two time delays into the system and Holling type-II functional response.The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number and time delays.Stability changes occur through Hopf-bifurcation when time delays cross the critical values.Optimal control theory has been applied for cost-effectiveness of the delayed system.Numerical simulations are carried out to justify the analytical results.This study shows that optimal farming awareness through radio,TV etc.can control the delay induced bifurcation in a cost-effective way.