scholarly journals Multiple coexistence states for a prey–predator system with cross-diffusion

2004 ◽  
Vol 197 (2) ◽  
pp. 315-348 ◽  
Author(s):  
Kousuke Kuto ◽  
Yoshio Yamada
Keyword(s):  
Cross Diffusion ◽  
Coexistence States ◽  
Predator System

Coexistence states in a cross-diffusion system of a predator–prey model with predator satiation term

2018 ◽  
Vol 28 (11) ◽  
pp. 2131-2159 ◽  
Author(s):  
Willian Cintra ◽  
Cristian Morales-Rodrigo ◽  
Antonio Suárez
Keyword(s):  
A Priori ◽  
Diffusion System ◽  
Predator Satiation ◽  
Linear Diffusion ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Coexistence States ◽  
Predator Model

In this paper, we study the existence and non-existence of coexistence states for a cross-diffusion system arising from a prey–predator model with a predator satiation term. We use mainly bifurcation methods and a priori bounds to obtain our results. This leads us to study the coexistence region and compare our results with the classical linear diffusion predator–prey model. Our results suggest that when there is no abundance of prey, the predator needs to be a good hunter to survive.

EFFECT OF CROSS-DIFFUSION ON A DIFFUSIVE PREY-PREDATOR SYSTEM—A NONLINEAR ANALYSIS

1996 ◽  
Vol 04 (02) ◽  
pp. 159-169 ◽  
Author(s):  
J. CHATTOPADHYAY ◽  
A.K. SARKAR ◽  
P.K. TAPASWI
Keyword(s):  
Nonlinear Analysis ◽  
Dissipative Structure ◽  
Wave Length ◽  
Liapunov Function ◽  
Local Instability ◽  
Cross Diffusion ◽  
Global Behaviour ◽  
System A ◽  
Predator System ◽  
Diffusive System

In this paper, we show that a simple prey-predator diffusive system may give rise to spontaneous emergence of dissipative structure (patchiness) only in the presence of cross-diffusion. The critical wave-length just sufficient to drive the system to local instability has been worked out. Moreover, by constructing a suitable Liapunov function, we have also investigated the global behaviour of the dissipative structure.

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