Plane waves in systems having an intrinsic time lag

Abstract

Time delays in many biochemical and ecological systems are intrinsic and can be approximately modeled as discrete. If diffusive forces are present in such systems and delayed inputs to the system also have an intrinsic space dependence, then we get a set of partial differential equatiosn with a discrete lag. This paper presents a general, more improved and fairly complete analysis of plane waves in systems with intrinsic time lags. In this paper, we identitfy four types of cr5itical points that can arise in such a system and consider simultaneous perturbations in a system parameter and the discrete time lag near such points. We develop two-parameter plane wave solutions using the reductive perturbation theory, discuss their stability and apply the results to an example predator-prey model. The presence of a time lag necessitates an iterative procedure for geting the desired solutions.