Dynamics of a periodic switched predator–prey system with impulsive harvesting and hibernation of prey population

In this study, we investigate a mathematical model that describes the interactive dynamics of a predator-prey system with different kinds of response function. The positivity, boundedness, and uniform persistence of the system are established. We investigate the biologically feasible singular points and their stability analysis. We perform a comparative study by considering different kinds of functional responses, which suggest that the dynamical behavior of the system remains unaltered, but the position of the bifurcation points altered. Our model system undergoes Hopf bifurcation with respect to the growth rate of the prey population, which indicates that a periodic solution occurs around a fixed point. Also, we observed that our predator-prey system experiences transcritical bifurcation for the prey population growth rate. By using normal form theory and center manifold theorem, we investigate the direction and stability of Hopf bifurcation. The biological implications of the analytical and numerical findings are also discussed in this study.

Download Full-text

EFFECT OF VIRAL INFECTION ON THE GENERALIZED GAUSE MODEL OF PREDATOR-PREY SYSTEM

Journal of Biological System ◽

10.1142/s0218339003000646 ◽

2003 ◽

Vol 11 (01) ◽

pp. 19-26 ◽

Cited By ~ 4

Author(s):

J. CHATTOPADHYAY ◽

A. MUKHOPADHYAY ◽

P. K. ROY

Keyword(s):

Viral Infection ◽

Specific Growth ◽

Dynamical Behavior ◽

Prey Population ◽

Predator Population ◽

Predator Prey ◽

Stability Behavior ◽

Force Of Infection ◽

Prey System ◽

Infected Prey

The generalized Gause model of predator-prey system is revisited with an introduction of viral infection on prey population. Stability behavior of such modified system is carried out to observe the change of dynamical behavior of the system. To substantiate the analytical results of this generalized susceptible prey, infected prey and predator population, numerical simulations of the model with specific growth and response functions are performed. Our observations suggest that the disease on prey population has a destabilizing or stabilizing effect depending on the level of force of infection and may act as a biological control for the persistence of the species.

Download Full-text

The Dynamics of an Impulsive Predator-Prey System with Stage Structure and Holling Type III Functional Response

Abstract and Applied Analysis ◽

10.1155/2015/183526 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Zhixiang Ju ◽

Yuanfu Shao ◽

Xiaolan Xie ◽

Xiangmin Ma ◽

Xianjia Fang

Keyword(s):

Functional Response ◽

Global Attractivity ◽

Stage Structure ◽

Biological Resource ◽

Predator Prey ◽

Analysis Techniques ◽

Type Iii ◽

Predator Prey Model ◽

Prey System ◽

Impulsive Harvesting

Based on the biological resource management of natural resources, a stage-structured predator-prey model with Holling type III functional response, birth pulse, and impulsive harvesting at different moments is proposed in this paper. By applying comparison theorem and some analysis techniques, the global attractivity of predator-extinction periodic solution and the permanence of this system are studied. At last, examples and numerical simulations are given to verify the validity of the main results.

Download Full-text

DYNAMIC COMPLEXITIES OF HOLLING TYPE II FUNCTIONAL RESPONSE PREDATOR–PREY SYSTEM WITH DIGEST DELAY AND IMPULSIVE HARVESTING ON THE PREY

International Journal of Biomathematics ◽

10.1142/s179352450900056x ◽

2009 ◽

Vol 02 (02) ◽

pp. 229-242 ◽

Cited By ~ 5

Author(s):

JIANWEN JIA ◽

HUI CAO

Keyword(s):

Time Delay ◽

Functional Response ◽

Impulsive Differential Equation ◽

Global Attractivity ◽

Sufficient Condition ◽

Type Ii ◽

Predator Prey ◽

Prey System ◽

Impulsive Harvesting ◽

Type Ii Functional Response

In this paper, we introduce and study Holling type II functional response predator–prey system with digest delay and impulsive harvesting on the prey, which contains with periodically pulsed on the prey and time delay on the predator. We investigate the existence and global attractivity of the predator-extinction periodic solutions of the system. By using the theory on delay functional and impulsive differential equation, we obtain the sufficient condition with time delay and impulsive perturbations for the permanence of the system.

Download Full-text