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Hair cells conduct auditory transduction in vertebrates. In lower vertebrates such as frogs and turtles, due to the active mechanism in hair cells, hair bundles(stereocilia) can be spontaneously oscillating or quiescent. Recently, the…

We study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: i) phase noise acting…

In this article, we propose a very efficient technique to enhance the dynamical robustness for a network of mean-field coupled oscillators experiencing aging transition. In particular, we present a control mechanism based on delayed…

We report a design of delay coupling for targeting desired synchronization in delay dynamical systems. We target synchronization, antisynchronization, lag-, antilag- synchronization, amplitude death (or oscillation death) and generalized…

A dead zone in the interaction between two dynamical systems is a region of their joint phase space where one system is insensitive to the changes in the other. These can arise in a number of contexts, and their presence in phase…

This study investigates the synchronization dynamics of coupled-oscillator systems in which some of the oscillators are damaged and lose their autonomous oscillations. The damaged elements are modeled using damped oscillators; thus, the…

Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in…

We propose a method for optimizing mutual coupling functions to achieve fast and global synchronization between a pair of weakly coupled limit-cycle oscillators. Our method is based on phase reduction that provides a concise low-dimensional…

We report our investigation on the input signal amplification in unidirectionally coupled monostable Duffing oscillators in one- and two-dimensions with first oscillator alone driven by a weak periodic signal. Applying a perturbation theory…

We numerically investigate the complex nonlinear dynamics for two independently coupled laser systems consisting of (i) mutually delay-coupled edge emitting diode lasers and (ii) injection-locked quantum nano-structures lasers. A…

We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the…

We explore analytically the oscillation quenching phenomena (amplitude death and oscillation death) in a coupled third order phase locked loop (PLL) both in periodic and chaotic mode. The phase locked loops are coupled through mean field…

Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary…

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…

We report a new experimental approach using an optoelectronic feedback loop to investigate the dynamics of oscillators coupled on large complex networks with arbitrary topology. Our implementation is based on a single optoelectronic…

Coupled oscillator networks underlie many biological systems, from cardiac cycles to circadian rhythms. Phase-reduced models such as the Kuramoto model have been widely used to study synchronization, but they typically assume that…

Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…

A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a…

We investigate the occurrence of collective dynamical states such as transient amplitude chimera, stable amplitude chimera and imperfect breathing chimera states in a \textit{locally coupled} network of Stuart-Landau oscillators. In an…

We study oscillatory and oscillation suppressed phases in coupled counter-rotating nonlinear oscillators. We demonstrate the existence of limit cycle, amplitude death, and oscillation death, and also clarify the Hopf, pitchfork, and…