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

Time delays can occur naturally or as transport lags in many physico-chemic al as well as biological systems. Incorporating them into a lumped paramete r system results in a system of first-order ordinary delay-differential equ ations (DDEs). In this paper, we develop two-parameter periodic solutions n ear a Hopf point in such systems using the general reductive perturbation t heory and apply the results to a nonisothermal chemical reactor with delaye d feedback. The paper suggests that the two-parameter result can be general ized to multiple time delays and other parameters. Results of this work can be useful in constructing plane wave solutions, rotating waves, phase sing ularity and other interesting phenomena for temporal kinetic systems with t ime delays.