Reviving Oscillations in Coupled Nonlinear Oscillators

By introducing a processing delay in the coupling, we find that it can effectively annihilate the quenching of oscillation, amplitude death (AD), in a network of coupled oscillators by switching the stability of AD. It revives the oscillation in the AD regime to retain sustained rhythmic functioning of the networks, which is in sharp contrast to the propagation delay with the tendency to induce AD. This processing delay-induced phenomenon occurs both with and without the propagation delay. Further this effect is rather general from two coupled to networks of oscillators in all known scenarios that can exhibit AD, and it has a wide range of applications where sustained oscillations should be retained for proper functioning of the systems.

Figure 1

Destabilizing the stable HSS in coupled system (1), $\tau =0$. (a) AD region enclosed by the critical stability curves ${\delta }_{c\pm }(K)$ and (b) The effect of processing delay $\delta$ on the AD region.

Figure 2

Destabilizing the stable HSS in coupled system (1), $\tau >0$. (a) The effect of processing delay $\delta$ on the AD island and (b) The ratio of the AD island area $R=S(\delta )/S(\delta =0)$ vs $\delta$.

Figure 3

Destabilizing the stable HSS in coupled system (3) with dynamic coupling [(a) and (b)] and (4) with conjugate coupling [(c) and (d)]. (a) and (c): The largest real part ${\lambda }_{R,\max }$ of $\lambda$ vs $K$ [34]. (b) and (d): the critical value ${\delta }_c$ vs. $w$.

Figure 4

Destabilizing the stable IHSS in two coupled Brusselators (5). (a)–(d) Solution diagrams of steady states, where red bold lines correspond to stable steady states and black thin lines to unstable ones. (e) The ratio of the length of stable IHSS interval $R=L(\delta )/L(\delta =0)$ vs $\delta$. The points with values of $\delta$ used in (a)–(d) are highlighted with red color.

Figure 5

Destabilizing the stable HSS in a network of delay-coupled oscillators, Eq. (6). $w_j=10$. (a) The effect of processing delay $\delta$ on AD island with ${\rho }_N=-0.96$. (b) The critical value ${\delta }_c$ linearly increasing as ${\rho }_N$ increases with the slope of 0.0313.