Generating and enhancing lag synchronization of chaotic systems by white noise

Enhancing coherence via tuning coupling range in nonlocally coupled Stuart-Landau oscillators

Nonlocal coupling, as an important connection topology among nonlinear oscillators, has attracted increasing attention recently with the research boom of chimera states. So far, most previous investigations have focused on nonlocally coupled systems interacted via similar variables. In this work, we report the evolutions of dynamical behaviors in the nonlocally coupled Stuart-Landau oscillators by applying conjugate variables feedback. Through rigorous analysis, we find that the oscillation death (OD) can convert into the amplitude death (AD) via the cluster state with the increasing of coupling range, making the AD regions to be expanded infinitely along two directions of both the natural frequency and the coupling strength. Moreover, the limit cycle oscillation (OS) region and the mixed region of OD and OS will turn to anti-synchronization state through amplitude-mediated chimera. Therefore, the procedure from local coupling to nonlocal one implies indeed the continuous enhancement of coherence among neighboring oscillators in coupled systems.

Explosive death of conjugate coupled Van der Pol oscillators on networks

Explosive death phenomenon has been gradually gaining attention of researchers due to the research boom of explosive synchronization, and it has been observed recently for the identical or nonidentical coupled systems in all-to-all network. In this work, we investigate the emergence of explosive death in networked Van der Pol (VdP) oscillators with conjugate variables coupling. It is demonstrated that the network structures play a crucial role in identifying the types of explosive death behaviors. We also observe that the damping coefficient of the VdP system not only can determine whether the explosive death state is generated but also can adjust the forward transition point. We further show that the backward transition point is independent of the network topologies and the damping coefficient, which is well confirmed by theoretical analysis. Our results reveal the generality of explosive death phenomenon in different network topologies and are propitious to promote a better comprehension for the oscillation quenching behaviors.

Modulating resonance behaviors by noise recycling in bistable systems with time delay

In this paper, the impact of noise recycling on resonance behaviors is studied theoretically and numerically in a prototypical bistable system with delayed feedback. According to the interior cooperating and interacting activity of noise recycling, a theory has been proposed by reducing the non-Markovian problem into a two-state model, wherein both the master equation and the transition rates depend on not only the current state but also the earlier two states due to the recycling lag and the feedback delay. By virtue of this theory, the formulae of the power spectrum density and the linear response function have been found analytically. And the theoretical results are well verified by numerical simulations. It has been demonstrated that both the recycling lag and the feedback delay play a crucial role in the resonance behaviors. In addition, the results also suggest an alternative scheme to modulate or control the coherence or stochastic resonance in bistable systems with time delay.

Resonance dynamics evoked via noise recycling procedure

We study the effect of noise recycling on nonequilibrium escape dynamics in a bistable system. For small noise, the non-Markovian problem is reduced to a two-state model with the master equation depending on not only the current state but also the earlier state, based on which we are able to derive the analytical formulas for the switching rate, the autocorrelation function, and the power spectrum density (PSD). Both the theoretical and the numerical results show that, with modulating the time delay in noise recycling, a monotonic PSD may switch to a nonmonotonic one; the amplitude of PSD at resonance frequency exhibits a pronounced maximum at a certain noise level, declaring the onset of stochastic resonance (SR) in the absence of a weak periodic signal. Further, we also demonstrate that the linear response to the external periodic force displays a maximum at a certain level of time delay, displaying the signature of SR.

Effects of noise on the outer synchronization of two unidirectionally coupled complex dynamical networks

We study the effect of noise on the outer synchronization between two unidirectionally coupled complex networks and find analytically that outer synchronization could be achieved via white-noise-based coupling. It is also demonstrated that, if two networks have both conventional linear coupling and white-noise-based coupling, the critical deterministic coupling strength between two complex networks for synchronization transition decreases with an increase in the intensity of noise. We provide numerical results to illustrate the feasibility and effectiveness of the theoretical results.