Positive steady state solutions of a Leslie–Gower predator–prey model with Holling type II functional response and density-dependent diffusion

2013 ◽  
Vol 82 ◽  
pp. 47-65 ◽  
Author(s):  
Jun Zhou
Keyword(s):  
Steady State ◽  
Functional Response ◽  
Type Ii ◽  
Predator Prey ◽  
Density Dependent ◽  
Predator Prey Model ◽  
Positive Steady State ◽  
Prey Model ◽  
Steady State Solutions ◽  
Type Ii Functional Response

scholarly journals Analysis of Stochastic Predator-Prey Model with Disease in the Prey and Holling Type II Functional Response

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
C. Gokila ◽  
M. Sambath ◽  
K. Balachandran ◽  
Yong-Ki Ma
Keyword(s):  
Functional Response ◽  
Lyapunov Functions ◽  
Stochastic Systems ◽  
Uniform Continuity ◽  
Type Ii ◽  
Equilibrium Solutions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Type Ii Functional Response

A stochastic predator-prey model with disease in the prey and Holling type II functional response is proposed and its dynamics is analyzed. We discuss the boundedness of the dynamical system and find all feasible equilibrium solutions. For the stochastic systems, we obtain the conditions for the existence of the global unique solution, boundedness, and uniform continuity. We derive the conditions for extinction and permanence of species. Moreover, we construct appropriate Lyapunov functions and discuss the asymptotic stability of equilibria. To illustrate our theoretical findings, we have performed numerical simulations and presented the results.

COMPLEXITY OF A DELAYED PREDATOR–PREY MODEL WITH IMPULSIVE HARVEST AND HOLLING TYPE II FUNCTIONAL RESPONSE

2008 ◽  
Vol 11 (01) ◽  
pp. 77-97 ◽  
Author(s):  
GUANGZHAO ZENG ◽  
FENGYAN WANG ◽  
JUAN J. NIETO
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Type Ii ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Delay Differential ◽  
Type Ii Functional Response

We study an impulsive delay differential predator–prey model with Holling type II functional response. The stability of the trivial equilibrium is analyzed by means of impulsive Floquet theory providing a sufficient condition for extinction. Using coincidence degree theory we show the existence of positive periodic solutions. The system is then analyzed numerically, revealing that the presence of delays and impulses may lead to chaotic solutions, quasi-periodic solutions, or multiple periodic solutions. Several simulations and examples are presented.

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