Dynamics and spatio-temporal patterns in a prey-predator system with aposematic prey

We analyze the impact of aposematic time and searching efficiency of prey on the temporal and spatio-temporal dynamics of a diffusive prey-predator system. Here, our assumption is that the prey population primarily invests its total time in two activities-(i) defense against predation and (ii) searching for food, followed by growth-induced reproduction, whereas, predators do not involve in self-defense. Moreover, we consider that the reproduction rate of prey and the rate of predation have a negative linear correlation with the amount of time invested for aposematism. Based on the presump- tions, we find that unlike searching efficiency of prey, the aposematic time can diminish the proportion in which prey and predator coexist when it crosses a certain threshold, and at the extreme aposematism, the entire population drives into the extinction. The proposed dynamics undergoes Hopf-bifurcation with respect to the searching efficiency of prey. We examine the individual effect of aposematic time and searching efficiency on the formation of regular Turing patterns-the low to medium to high val-ues of defense-time and food searching efficiency generate 'spots' to 'stripes' to 'holes' pattern, re-spectively; however, the combined impact of both presents only non-Turing 'spot' pattern with the 'predominance of predators,' which happens through the Turing-Hopf bifurcation.