Shi Qingyan, Shi Junping, Wang Hao
School of Science, Jiangnan University, Wuxi, 214122, Jiangsu, China.
Department of Mathematics, William & Mary, Williamsburg, VA, 23187-8795, USA.
J Math Biol. 2021 Mar 11;82(4):33. doi: 10.1007/s00285-021-01588-0.
Diffusion has been widely applied to model animal movement that follows Brownian motion. However, animals typically move in non-Brownian ways due to their perceptual judgment. Spatial memory and cognition recently have received much attention in characterizing complicated animal movement behaviours. Explicit spatial memory is modeled via a distributed delayed diffusion term in this paper. The distributed time represents the memory growth and decay over time, and the spatial nonlocality reflects the dependence of spatial memory on location. When the temporal delay kernel is weak under the assumption that animals can immediately acquire knowledge and memory decays over time, the equation is equivalent to a Keller-Segel chemotaxis model. For the strong kernel with learning and memory decay stages, rich spatiotemporal dynamics, such as Turing and checker-board patterns, appear via spatially non-homogeneous steady-state and Hopf bifurcations.
扩散已被广泛应用于对遵循布朗运动的动物运动进行建模。然而，由于动物的感知判断，它们通常以非布朗方式移动。空间记忆和认知最近在表征复杂的动物运动行为方面受到了广泛关注。本文通过一个分布式延迟扩散项对显式空间记忆进行建模。分布式时间表示记忆随时间的增长和衰减，而空间非局部性反映了空间记忆对位置的依赖性。当在动物能够立即获取知识且记忆随时间衰减的假设下时间延迟核较弱时，该方程等同于一个凯勒 - 西格尔趋化模型。对于具有学习和记忆衰减阶段的强核，通过空间非均匀稳态和霍普夫分岔会出现丰富的时空动力学，如图灵模式和棋盘模式。
