TY - JOUR
T1 - The spatial patterns through diffusion-driven instability in a predator-prey model
AU - Guin, Lakshmi Narayan
AU - Haque, Mainul
AU - Mandal, Prashanta Kumar
N1 - Funding Information:
The final form of the paper owes much to the helpful suggestions of the referees, whose careful scrutiny we are pleased to acknowledge. The authors (L.N.G., P.K.M.) gratefully acknowledge the financial support in part from Special Assistance Programme (SAP-II) sponsored by the University Grants Commission (UGC), New Delhi, India.
PY - 2012/5
Y1 - 2012/5
N2 - Studies on stability mechanism and bifurcation analysis of a system of interacting populations by the combined effect of self and cross-diffusion become an important issue in ecology. In the current investigation, we derive the conditions for existence and stability properties of a predator-prey model under the influence of self and cross-diffusion. Numerical simulations have been carried out in order to show the significant role of self and cross-diffusion coefficients and other important parameters of the system. Various contour pictures of spatial patterns through Turing instability are portrayed and analysed in order to substantiate the applicability of the present model. Finally, the paper ends with an extended discussion of biological implications of our findings.
AB - Studies on stability mechanism and bifurcation analysis of a system of interacting populations by the combined effect of self and cross-diffusion become an important issue in ecology. In the current investigation, we derive the conditions for existence and stability properties of a predator-prey model under the influence of self and cross-diffusion. Numerical simulations have been carried out in order to show the significant role of self and cross-diffusion coefficients and other important parameters of the system. Various contour pictures of spatial patterns through Turing instability are portrayed and analysed in order to substantiate the applicability of the present model. Finally, the paper ends with an extended discussion of biological implications of our findings.
KW - Diffusion-driven instability
KW - Hopf-bifurcation
KW - Predator-prey model
KW - Reaction-diffusion system
KW - Self and cross-diffusion
KW - Simulation
UR - http://www.scopus.com/inward/record.url?scp=84855846335&partnerID=8YFLogxK
U2 - 10.1016/j.apm.2011.05.055
DO - 10.1016/j.apm.2011.05.055
M3 - Article
AN - SCOPUS:84855846335
SN - 0307-904X
VL - 36
SP - 1825
EP - 1841
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
IS - 5
ER -