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.
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