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Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand…
Coupling of chaotic oscillators has evidenced conditions where synchronization is possible, therefore a nonlinear system can be driven to a particular state through input from a similar oscillator. Here we expand this concept of control of…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable…
We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the…
The concept of out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is…
In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others…
Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the…
The synchronous dynamics of an array of excitable oscillators, coupled via a generic graph, is studied. Non homogeneous perturbations can grow and destroy synchrony, via a self-consistent instability which is solely instigated by the…
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…
This paper gives sufficient conditions for having complete synchronization of oscillators in connected undirected networks. The considered oscillators are not necessarily identical and the synchronization terms can be nonlinear. An…
We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. This…
We present an extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks. In the synchronization process, different structures corresponding to…
We explore the interplay of network structure, topology, and dynamic interactions between nodes using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state,…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
We have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. By considering firstly the neuronal system as an example, we show that this theoretical approach can predict…
We consider the problem of maximizing the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. We first extend the well-known master stability formalism to the case of…
We analyze the synchronization dynamics of phase oscillators far from the synchronization manifold, including the onset of synchronization on scale-free networks with low and high clustering coefficients. We use normal coordinates and…