A death of oscillation is reported in a network of coupled synchronized oscillators in presence of additional repulsive coupling. The repulsive link evolves as an averaging effect of mutual interaction between two neighboring oscillators due to a local fault and the number of repulsive links grows in time when the death scenario emerges. Analytical condition for oscillation death is derived for two coupled Landau-Stuart systems. Numerical results also confirm oscillation death in chaotic systems such as a Sprott system and the Rössler oscillator. We explore the effect in large networks of globally coupled oscillators and find that the number of repulsive links is always fewer than the size of the network.A quenching or death of oscillation is an important phenomenon [1-3] in coupled oscillators (limit cycle or chaotic) besides synchronization [4]. It is mainly dictated by large parameter mismatch in coupled oscillators [5] or delay in coupling [6] of identical oscillators. In recent times, several other mechanisms of oscillation death or stabilization of fixed point were reported using different coupling schemes which were based on dynamic coupling [7], mean field diffusion coupling [8,9] and conjugate coupling [10] in identical oscillators, and dynamic environment coupling [11] in identical or mismatched oscillators. Of particular interest is the dynamic environment coupling [11] that is able to induce oscillation death in a network [12], chain, ring, tree, lattice, all-to-all, star, and random topologies. An over-damped dynamic environment influences each of the dynamical units in a network and suppresses the oscillation of all the units for a critical coupling.In real world, a different situation may arise when besides the diffusive attractive coupling between the dynamical nodes that establishes a priori synchrony in a network of oscillators, additional coupling links or bonds evolve in time between two neighboring nodes in the network due to a local disturbance or a fault. This local fault can act as a repulsive feedback link on an immediate local node. We assume that the number of repulsive links increases in time to spread into the other nodes of the network. Eventually, the increasing repulsive links influence the dynamics of the network in time and induce a death situation as quenching of oscillation much before it spreads into the whole network. The concept of all-to-all additional dynamic environment coupling or links [12] cannot explain such a situation since only a fewer nodes than the size of the network are locally affected by the additional repulsive links and suffice to induce a death. We mention that a quenching of oscillation, although in a different context but of similar effect, was reported earlier as an aging transition [13] when, in a network of diffusively coupled oscillators, individual oscillators switch over to a passive state or excitable state one after another in time and that the oscillation in the network eventually comes to a stop when a sufficient number of oscillators switches...

We observe extremely large amplitude intermittent spikings in a dynamical variable of a periodically forced Liénard-type oscillator and characterize them as extreme events, which are rare, but recurrent and larger in amplitude than a threshold. The extreme events occur via two processes, an interior crisis and intermittency. The probability of occurrence of the events shows a long-tail distribution in both the cases. We provide evidence of the extreme events in an experiment using an electronic analog circuit of the Liénard oscillator that shows good agreement with our numerical results.

We study excitation and suppression of chimera states in an ensemble of nonlocally coupled oscillators arranged in a framework of multiplex network. We consider the homogeneous network (all identical oscillators) with different parametric cases and interlayer heterogeneity by introducing parameter mismatch between the layers. We show the feasibility to suppress chimera states in the multiplex network via moderate interlayer interaction between a layer exhibiting chimera state and other layers which are in a coherent or incoherent state. On the contrary, for larger interlayer coupling, we observe the emergence of identical chimera states in both layers which we call an interlayer chimera state. We map the spatiotemporal behavior in a wide range of parameters, varying interlayer coupling strength and phase lag in two and three multiplexing layers. We also prove the emergence of interlayer chimera states in a multiplex network via evaluation of a continuous model. Furthermore, we consider the two-layered network of Hindmarsh-Rose neurons and reveal that in such a system multiplex interaction between layers is capable of exciting not only the synchronous interlayer chimera state but also nonidentical chimera patterns.

We present a general bifurcation in the synchronized dynamics of time-delay-coupled nonlinear oscillators. The relative phase between the oscillators jumps from zero to pi as a function of the coupling; this phase-flip bifurcation is accompanied by a discontinuous change in the frequency of the synchronized oscillators. This phenomenon is of broad relevance, being observed in regimes of oscillator death as well as in periodic, quasiperiodic, and chaotic dynamics. Time-delay coupling is necessary for the phase-flip bifurcation. We illustrate the phenomenon, and present analytical results for paradigmatic nonlinear systems. Possible applications are discussed.

We propose a design of coupling for stable synchronization and antisynchronization in chaotic systems under parameter mismatch. The antisynchronization is independent of the specific symmetry (reflection symmetry, axial symmetry, or other) of a dynamical system. In the synchronization regimes, we achieve amplification (attenuation) of a chaotic driver in a response oscillator. Numerical examples of a Lorenz system, Rössler oscillator, and Sprott system are presented. Experimental evidence is shown using an electronic version of the Sprott system.

We present evidence of extreme events in two Hindmarsh-Rose (HR) bursting neurons mutually interacting via two different coupling configurations: chemical synaptic- and gap junctional-type diffusive coupling. A dragon-king-like probability distribution of the extreme events is seen for combinations of synaptic coupling where small- to medium-size events obey a power law and the larger events that cross an extreme limit are outliers. The extreme events originate due to instability in antiphase synchronization of the coupled systems via two different routes, intermittency and quasiperiodicity routes to complex dynamics for purely excitatory and inhibitory chemical synaptic coupling, respectively. For a mixed type of inhibitory and excitatory chemical synaptic interactions, the intermittency route to extreme events is only seen. Extreme events with our suggested distribution is also seen for gap junctional-type diffusive, but repulsive, coupling where the intermittency route to complexity is found. A simple electronic experiment using two diffusively coupled analog circuits of the HR neuron model, but interacting in a repulsive way, confirms occurrence of the dragon-king-like extreme events.

Recently, the phase-flip bifurcation has been described as a fundamental transition in time-delay coupled, phase-synchronized nonlinear dynamical systems. The bifurcation is characterized by a change of the synchronized dynamics from being in-phase to antiphase, or vice versa; the phase-difference between the oscillators undergoes a jump of pi as a function of the coupling strength or the time delay. This phase-flip is accompanied by discontinuous changes in the frequency of the synchronized oscillators, and in the largest negative Lyapunov exponent or its derivative. Here we illustrate the phenomenology of the bifurcation for several classes of nonlinear oscillators, in the regimes of both periodic and chaotic dynamics. We present extensive numerical simulations and compute the oscillation frequencies and the Lyapunov spectra as a function of the coupling strength. In particular, our simulations provide clear evidence of the phase-flip bifurcation in excitable laser and Fitzhugh-Nagumo neuronal models, and in diffusively coupled predator-prey models with either limit cycle or chaotic dynamics. Our analysis demonstrates marked jumps of the time-delayed and instantaneous fluxes between the two interacting oscillators across the bifurcation; this has strong implications for the performance of the system as well as for practical applications. We further construct an electronic circuit consisting of two coupled Chua oscillators and provide the first formal experimental demonstration of the bifurcation. In totality, our study demonstrates that the phase-flip phenomenon is of broad relevance and importance for a wide range of physical and natural systems.

We observe chimeralike states in an ensemble of oscillators using a type of global coupling consisting of two components: attractive and repulsive mean-field feedback. We identify existence of two types of chimeralike states in a bistable Liénard system; in one type, both the coherent and the incoherent populations are in chaotic states (called as chaos-chaos chimeralike states) and, in another type, the incoherent population is in periodic state while the coherent population has irregular small oscillation. Interestingly, we also recorded a metastable state in a parameter regime of the Liénard system where the coherent and noncoherent states migrates from one to another population. To test the generality of the coupling configuration, we present another example of bistable system, the van der Pol-Duffing system where the chimeralike states are observed, however, the coherent population is periodic or quasiperiodic and the incoherent population is of chaotic in nature. Furthermore, we apply the coupling to a network of chaotic Rössler system where we find the chaos-chaos chimeralike states.