Related papers: Embedding the dynamics of a single delay system in…
A system of ODE's is used to approximate the dynamics of two delayed coupled FitzHugh-Nagumo excitable units, and study the relevant bifurcations. It is shown that the Bautin bifurcation acts as the organizing center for the dynamics of…
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 consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial…
Many systems of physical and biological interest are characterized by assemblies of phase oscillators whose interaction is mediated by a diffusing chemical. The coupling effect results from the fact that the local concentration of the…
We consider an ensemble of globally coupled phase oscillators whose interaction is transmitted at finite speed. This introduces time delays, which make the spatial coordinates relevant in spite of the infinite range of the interaction. We…
Many real-world examples of distributed oscillators involve not only time delays but also attractive (positive) and repulsive (negative) influences in their network interactions. Here, considering such examples, we generalize the Kuramoto…
We investigate pattern formation in self-oscillating systems forced by an external periodic perturbation. Experimental observations and numerical studies of reaction-diffusion systems and an analysis of an amplitude equation are presented.…
We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics…
We study the quantum and classical scattering of Hamiltonian systems whose chaotic saddle is described by binary or ternary horseshoes. We are interested in parameters of the system for which a stable island, associated with the inner…
We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these…
Microresonators are micron-scale optical systems that confine light using total internal reflection. These optical systems have gained interest in the last two decades due to their compact sizes, unprecedented measurement capabilities, and…
Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are…
We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which…
We study the effects of delayed coupling on timing and pattern formation in spatially extended systems of dynamic oscillators. Starting from a discrete lattice of coupled oscillators, we derive a generic continuum theory for collective…
We derive the normal form for the delay-induced Hopf bifurcation in the first-order phase-locked loop with time delay by the multiple scaling method. The resulting periodic orbit is confirmed by numerical simulations. Further detailed…
We study the dynamics of photonic quantum circuits consisting of nodes coupled by quantum channels. We are interested in the regime where time delay in communication between the nodes is significant. This includes the problem of quantum…
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…
This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with quadratic term and delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try…
Demographic oscillators are individual-based systems exhibiting temporal cycles sustained by the stochastic dynamics of the microscopic interacting particles. We here use the example of coupled predator-prey oscillators to show that…
We investigate the stability of the synchronization manifold in a ring and an open-ended chain of nearest neighbors coupled self-sustained systems, each self-sustained system consisting of multi-limit cycles van der Pol oscillators. Such…