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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 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.

We report the first experimental observation of extreme multistability in a controlled laboratory investigation. Extreme multistability arises when infinitely many attractors coexist for the same set of system parameters. The behavior was predicted earlier on theoretical grounds, supported by numerical studies of models of two coupled identical or nearly identical systems. We construct and couple two analog circuits based on a modified coupled Rössler system and demonstrate the occurrence of extreme multistability through a controlled switching to different attractor states purely through a change in initial conditions for a fixed set of system parameters. Numerical studies of the coupled model equations are in agreement with our experimental findings.