Comptes rendus de l’Acade'mie bulgare des Sciences, Vol 60, No2, pp.127-132

CHAOS IN A DELAYED PROTEIN CROSS TALK MODEL WITH PERIODIC FORCING

S.Nikolov, J.Vera, O.Wolkenhauer, E.Yankulova, V.Petrov

ABSTRACT

The e®ects of periodic forcing on the time delay protein cross talk model are investigated. We assume periodic variation for plasma membrane permeabilities. The dynamic behaviour of the system is simulated and bifurcation diagrams are obtained for di®erent parameters. The results show that periodic forcing can very easily give rise to complex dynamics, including a period-doubling cascade, chaos, quasi-periodic oscillating, and periodic windows. Finally, we calculate the maximal Lyapunov exponent in the regions of the parameter space where chaotic motion of delayed protein cross talk model with periodic forcing exists.

Key words: chaotic behaviour, time delay, protein cross talk, maximal Lyapunov exponent

Topic: PHYSICS