Dynamics and dissipation in an externally forced system

Abstract

We study numerically the influence of periodic and random external perturbations on the oscillating Selkov model by varying one dimensionless parameter, κ, of the model. When the variations of κ are periodic in time, the system responds with bursting oscillations in the case where the forcing frequency is different from the frequency of the oscillations without any perturbations. When the frequencies are almost equal, the system responds to the forcing by oscillating with almost the same frequency as the forcing, but with a higher amplitude linearly proportional to the amplitude of the perturbation. In the second case, κ varies randomly with time. The dynamics are described by stochastic differential equations. The computed ensemble averages of concentrations exhibit a decay or localization of the limit cycle for small amplitudes of the noise. This decay is faster when the amplitude of the noise is higher. As the noise amplitude increases, chaotic behavior begins to appear. For noise amplitudes high enough to push the system away from the oscillatory region, the system exhibits high-amplitude intermittent bursts in the concentrations for different realizations of the noise. We also computed the chemical entropy production for all the cited cases. When κ varies periodically with the same frequency, the entropy production increases nonlinearly with the amplitude of the forcing; the amplitude of the oscillations increases only linearly with the amplitude of the forcing. In general, when the system is periodically forced, strips of high dissipation and valleys of low dissipation exist in the space formed by the amplitude of the perturbation and winding number. In the second case, where κ is random the overall average entropy production is insensitive to the amplitude of the noise as long as κ does not leave the oscillatory region. When κ begins to cross into other regions, the overall average entropy production increases almost linearly with the amplitude of the noise.