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Pattern formation in a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth. (English) Zbl 1264.34169
Summary: The spatiotemporal dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth subject to zero-flux boundary condition are investigated analytically and numerically. The asymptotic stability of the positive equilibrium and the existence of Hopf bifurcation around the positive equilibrium are shown; the conditions of Turing instability are obtained. And with the help of numerical simulations, it is found that the model exhibits complex pattern replication: stripes, spots-stripes mixtures, and spots Turing patterns.

MSC:
34K60Qualitative investigation and simulation of models
34K18Bifurcation theory of functional differential equations
34K20Stability theory of functional-differential equations
92D25Population dynamics (general)
Software:
PRED_PREY
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Full Text: DOI
References:
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