Title：Global dynamics and spatio temporal heterogeneity of accelerated preytaxis models

Speaker：Prof. Zhian Wang (Hong Kong Polytechnic University)

Time:Thursday,December 16, 2021,PM:3:00-4:00

Tencent Conference:250812765

Inviter：Prof. Haiyang Jin

Abstract：Conventional preytaxis systems assume that preytactic velocity is proportional to the prey density gradient. However many experiments exploring the predator-prey interactions show it is the predator's acceleration instead of velocity that is proportional to the prey density gradient in the preytactic movement, which we call non-conventional preytaxis. Mathematical models of non-conventional preytaxis were proposed in the literature to interpret the spatial heterogeneity of predators and prey observed in experiments. We shall explore the qualitative behavior of such non-conventional preytaxis systems and establish the global existence of classical solutions with uniform-in-time bound in any spatial dimensions. Moreover we prove the global stability of spatially homogeneous prey-only and coexistence steady states with decay rates under certain conditions on system parameters. For the parameters outside the stability regime, we perform linear stability analysis to find the possible patterning regimes and use numerical simulations to demonstrate that spatially inhomogeneous time-periodic patterns will typically arise from the non-conventional preytaxis system. Noticing that conventional preytaxis systems are unable to produce spatial patterns, our results imply that the non-conventional preytaxis is indeed more appropriate than conventional preytaxis to interpret the spatial heterogeneity resulting from the predator-prey interactions.