Related papers: Multistability of globally coupled Duffing oscilla…
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
Clustered solutions in oscillator networks provide an important insight into how a system might diversify from a synchronous solution into spatiotemporal complex solutions. They can therefore form a link between fully synchronized and…
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which \textit{unstable…
This paper studies the dynamics of a network of diffusively-coupled bistable systems. Under mild conditions and without requiring smoothness of the vector field, we analyze the network dynamics and show that the solutions converge globally…
We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can…
Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the…
We consider an ensemble of coupled oscillators whose individual states, in addition to the phase, are characterized by an internal variable with autonomous evolution. The time scale of this evolution is different for each oscillator, so…
We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled…
We demonstrate emergence of a complex state in a homogeneous ensemble of globally coupled identical oscillators, reminiscent of chimera states in locally coupled oscillator lattices. In this regime some part of the ensemble forms a…
We study the noisy dynamics of two coupled bistable modes of a nanomechanical beam. When de-coupled, each driven mode obeys the Duffing equation of motion, with a well-defined bistable region in the frequency domain. When both modes are…
Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in…
The widespread phenomena of multistability is a problem involving rich dynamics to be explored. In this paper, we study the multistability of a generalized nonlinear forcing oscillator excited by $f(x)cos \omega t$. We take Doubochinski's…
Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the…
Adaptive dynamical networks are ubiquitous in real-world systems. This paper aims to explore the synchronization dynamics in networks of adaptive oscillators based on a paradigmatic system of adaptively coupled phase oscillators. Our…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
This paper studies the stability of synchronized states in networks where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of…
Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder - diversity of intrinsic oscillatory frequencies and external independent noise.…
This paper considers the cluster synchronization problem of generic linear dynamical systems whose system models are distinct in different clusters. These nonidentical linear models render control design and coupling conditions highly…