scholarly journals LONG-TIME PROPERTIES OF PREY-PREDATOR SYSTEM WITH CROSS-DIFFUSION

2006 ◽  
Vol 21 (2) ◽  
pp. 293-320 ◽  
Author(s):  
Seong-A Shim
Keyword(s):  
Cross Diffusion ◽  
Long Time ◽  
Predator System

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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