Two-parameter periodic solutions near a Hopf point in delay-differential equations

Abstract

Time delays can occur naturally or as transport lags in many physico-chemical as well as biological systems. Incorporating them into a lumped parameter system results in a system of first-order ordinary delay-differential equations (DDEs). In this paper, we develop two-parameter periodic solutions near a Hopf point in such systems using the general reductive perturbation theory and apply the results to a nonisothermal chemical reactor with delayed feedback. The paper suggests that the two-parameter result can be generalized to multiple time delays and other parameters. Results of this work can be useful in constructing plane wave solutions, rotating waves, phase singularity and other interesting phenomena for temporal kinetic systems with time delays.