scholarly journals Positive steady states for a prey-predator cross-diffusion system with a protection zone and Holling type II functional response

2013 ◽  
Keyword(s):  
Functional Response ◽  
Steady States ◽  
Diffusion System ◽  
Type Ii ◽  
Protection Zone ◽  
Cross Diffusion ◽  
Positive Steady States ◽  
Type Ii Functional Response

scholarly journals Steady state for a predator–prey cross-diffusion system with the Beddington–DeAngelis and Tanner functional response

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Demou Luo
Keyword(s):  
Fixed Point ◽  
Functional Response ◽  
Fixed Point Index ◽  
Index Theory ◽  
Diffusion System ◽  
Point Index ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Fixed Point Index Theory ◽  
Positive Steady States

AbstractThe main goal of this paper is investigating the existence of nonconstant positive steady states of a linear prey–predator cross-diffusion system with Beddington–DeAngelis and Tanner functional response. An analytical method and fixed point index theory plays a significant role in our main proofs.

Predator-dependent transmissible disease spreading in prey under Holling type-II functional response

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dipankar Ghosh ◽  
Prasun K. Santra ◽  
Abdelalim A. Elsadany ◽  
Ghanshaym S. Mahapatra
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Linearization Method ◽  
Logistic Growth ◽  
Type Ii ◽  
Disease Spreading ◽  
Predator Interactions ◽  
The Stability ◽  
Infected Prey ◽  
Type Ii Functional Response

Abstract This paper focusses on developing two species, where only prey species suffers by a contagious disease. We consider the logistic growth rate of the prey population. The interaction between susceptible prey and infected prey with predator is presumed to be ruled by Holling type II and I functional response, respectively. A healthy prey is infected when it comes in direct contact with infected prey, and we also assume that predator-dependent disease spreads within the system. This research reveals that the transmission of this predator-dependent disease can have critical repercussions for the shaping of prey–predator interactions. The solution of the model is examined in relation to survival, uniqueness and boundedness. The positivity, feasibility and the stability conditions of the fixed points of the system are analysed by applying the linearization method and the Jacobian matrix method.

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