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Allee effect in population dynamics has a major impact in suppressing theparadox of enrichment through global bifurcation, and it can generate highlycomplex dynamics. The influence of the reproductive Allee effect, incorporatedin the prey's growth rate of a prey-predator model with Beddington-DeAngelisfunctional response, is investigated here. Preliminary local and globalbifurcations are identified of the temporal model. Existence and non-existenceof heterogeneous steady-state solutions of the spatio-temporal system areestablished for suitable ranges of parameter values. The spatio-temporal modelsatisfies Turing instability conditions, but numerical investigation revealsthat the heterogeneous patterns corresponding to unstable Turing eigen modesacts as a transitory pattern. Inclusion of the reproductive Allee effect in theprey population has a destabilising effect on the coexistence equilibrium. Fora range of parameter values, various branches of stationary solutions includingmode-dependent Turing solutions and localized pattern solutions are identifiedusing numerical bifurcation technique. The model is also capable to producesome complex dynamic patterns such as travelling wave, moving pulse solution,and spatio-temporal chaos for certain range of parameters and diffusivity alongwith appropriate choice of initial conditions Judicious choices ofparametrization for the Beddington-DeAngelis functional response help us toinfer about the resulting patterns for similar prey-predator models withHolling type-II functional response and ratio-dependent functional response.

Analytical detection of stationary and dynamic patterns in a prey-predator model with reproductive Allee effect in prey growth