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
2018 ◽  
Vol 28 (11) ◽  
pp. 2131-2159 ◽  
Author(s):  
Willian Cintra ◽  
Cristian Morales-Rodrigo ◽  
Antonio Suárez

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.


1996 ◽  
Vol 04 (02) ◽  
pp. 159-169 ◽  
Author(s):  
J. CHATTOPADHYAY ◽  
A.K. SARKAR ◽  
P.K. TAPASWI

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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