Effect of asymmetry parameter on the dynamical states of nonlocally coupled nonlinear oscillators

Amplitude-mediated chimera states in nonlocally coupled Stuart-Landau oscillators

Chimera states achieve the coexistence of coherent and incoherent subgroups through symmetry breaking and emerge in physical, chemical, and biological systems. We show the presence of amplitude-mediated multicluster chimera states in nonlocally coupled Stuart-Landau oscillators. We clarify the prerequisites for having different types of chimera states by analytically and numerically studying how phase transitions occur between these states. Our results demonstrate how the oscillation amplitudes interact with the phase degrees of freedom in chimera states and significantly advance our understanding of the generation mechanisms of such states in coupled oscillator systems.

Chimera states and intermittency in an ensemble of nonlocally coupled Lorenz systems

We study the spatiotemporal dynamics of coupled Lorenz systems with nonlocal interaction and for small values of the coupling strength. It is shown that due to the interaction the effective values of the control parameters can shift and the classical quasi-hyperbolic Lorenz attractor in an isolated element is transformed to a nonhyperbolic one. In this case, the network becomes multistable that is a typical property of nonhyperbolic chaotic systems. This fact gives rise to the appearance of chimera-like states, which have not been found in the studied network before. We also reveal and describe three different types of intermittency, both in time and in space, between various spatiotemporal structures in the network of nonlocally coupled Lorenz models.

Mobility-induced persistent chimera states

We study the dynamics of mobile, locally coupled identical oscillators in the presence of coupling delays. We find different kinds of chimera states in which coherent in-phase and antiphase domains coexist with incoherent domains. These chimera states are dynamic and can persist for long times for intermediate mobility values. We discuss the mechanisms leading to the formation of these chimera states in different mobility regimes. This finding could be relevant for natural and technological systems composed of mobile communicating agents.

Implementation of dynamic dual input multiple output logic gate via resonance in globally coupled Duffing oscillators

We have used a system of globally coupled double-well Duffing oscillators under an enhanced resonance condition to design and implement Dual Input Multiple Output (DIMO) logic gates. In order to enhance the resonance, the first oscillator in the globally coupled system alone is excited by two forces out of which one acts as a driving force and the other will be either sub-harmonic or super-harmonic in nature. We report that for an appropriate coupling strength, the second force coherently drives and enhances not only the amplitude of the weak first force to all the coupled systems but also drives and propagates the digital signals if any given to the first system. We then numerically confirm the propagation of any digital signal or square wave without any attenuation under an enhanced resonance condition for an amplitude greater than a threshold value. Further, we extend this idea for computing various logical operations and succeed in designing theoretically DIMO logic gates such as AND/NAND, OR/NOR gates with globally coupled systems.

Basin stability for chimera states

Chimera states, namely complex spatiotemporal patterns that consist of coexisting domains of spatially coherent and incoherent dynamics, are investigated in a network of coupled identical oscillators. These intriguing spatiotemporal patterns were first reported in nonlocally coupled phase oscillators, and it was shown that such mixed type behavior occurs only for specific initial conditions in nonlocally and globally coupled networks. The influence of initial conditions on chimera states has remained a fundamental problem since their discovery. In this report, we investigate the robustness of chimera states together with incoherent and coherent states in dependence on the initial conditions. For this, we use the basin stability method which is related to the volume of the basin of attraction, and we consider nonlocally and globally coupled time-delayed Mackey-Glass oscillators as example. Previously, it was shown that the existence of chimera states can be characterized by mean phase velocity and a statistical measure, such as the strength of incoherence, by using well prepared initial conditions. Here we show further how the coexistence of different dynamical states can be identified and quantified by means of the basin stability measure over a wide range of the parameter space.

Spatiotemporal dynamics of the Kuramoto-Sakaguchi model with time-dependent connectivity

We study the dynamics of the paradigmatic Kuramoto-Sakaguchi model of identical coupled phase oscillators with various kinds of time-dependent connectivity using Eulerian discretization. We explore the parameter spaces for various types of collective states using the phase plots of the two statistical quantities, namely, the strength of incoherence and the discontinuity measure. In the quasistatic limit of the changing of coupling range, we observe how the system relaxes from one state to another and identify a few interesting collective dynamical states along the way. Under a sinusoidal change of the coupling range, the global order parameter characterizing the degree of synchronization in the system is shown to undergo a hysteresis with the coupling range. We also study the low-dimensional spatiotemporal dynamics of the local order parameter in the continuum limit using the recently developed Ott-Antonsen ansatz and justify some of our numerical results. In particular, we identify an intrinsic time scale of the Kuramoto system and show that the simulations exhibit two distinct kinds of qualitative behavior in two cases when the time scale associated with the switching of the coupling radius is very large compared to the intrinsic time scale and when it is comparable to the intrinsic time scale.