Advection-Diffusion Equations for Internal State-Mediated Random Walks

Abstract. In many biological examples of biased random walks, movement statistics are determined by state dynamics that are internal to the organism or cell and that mediate responses to variable environments. Internal state dynamics are an essential element of such behaviors because they provide a "memory" mechanism for retaining effects of previous environments over multiple iterations of the random walk, and because they impose constraints on the gradient-climbing movements that can result. When spatial gradients in individual density and in environmental properties are small, the timescales characterizing redistribution of populations over large spatial scales are typically much larger than those characterizing equilibration in the internal state and in orientation. Taking advantage of this difference in timescales, an advection-diffusion equation is derived that approximates the long-term spatial redistribution of individuals performing a velocity-jump process in which t...

• Type: Journal
• Year: 2000
• Where: SIAMAM
• Authors: Daniel Grünbaum
• Keywords: Advection-diffusion Equations, Internal State, Internal State Dynamics, SIAMAM 2000