Related papers: Controlled Perturbation-Induced Switching in Pulse…

We report the study of sudden transitions or tipping in a collection of systems induced due to multiplexing with another network of systems. The emergent dynamics of oscillators on one layer can undergo a sudden transition to steady state…

A network of coupled time-varying systems, where individual nodes are interconnected through links, is a modeling framework widely used by many disciplines. For identical nodes displaying a complex behavior known as chaos, clusters of nodes…

Synchronized oscillations are of critical functional importance in many biological systems. We show that such oscillations can arise without centralized coordination in a disordered system of electrically coupled excitable and passive…

Cluster synchronization is of paramount importance for the normal functioning of numerous technological and natural systems. Deviations from normal cluster synchronization patterns are closely associated with various malfunctions, such as…

We study a pulse-coupled dynamics of excitable elements in uncorrelated scale-free networks. Regimes of self-sustained activity are found for homogeneous and inhomogeneous couplings, in which the system displays a wide variety of behaviors,…

Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological…

The impact of control sequences on the environmental coupling of a quantum system can be described in terms of a filter. Here we analyze how the coherent evolution of two interacting spins subject to periodic control pulses, at the example…

We study a system of dynamical units, each of which shows excitable or oscillatory behavior, depending on the choice of parameters. When we couple these units with repressive bonds, we can control the duration of collective oscillations for…

We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…

Brain dynamics can exhibit narrow-band nonlinear oscillations and multistability. For a subset of disorders of consciousness and motor control, we hypothesize that some symptoms originate from the inability to spontaneously transition from…

Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units,…

We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the…

In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multi-cluster patterns,…

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…

We report the phenomenon of frequency clustering in a network of Hodgkin-Huxley neurons with spike timing-dependent plasticity. The clustering leads to a splitting of a neural population into a few groups synchronized at different…

Key features of biological activity can often be captured by transitions between a finite number of semi-stable states that correspond to behaviors or decisions. We present here a broad class of dynamical systems that are ideal for modeling…

We characterize the synchronization of an array of coupled chaotic elements as a phase transition where order parameters related to the joint probability at two sites obey power laws versus the mutual coupling strength; the phase transition…

This work provides new insights on the convergence of a locally connected network of pulse coupled oscillator (PCOs) (i.e., a bio-inspired model for communication networks) to synchronous and desynchronous states, and their implication in…

The synchronized activity of neuronal populations can lead to pathological over-synchronization in conditions such as epilepsy and Parkinson disease. Such states can be desynchronized by brief electrical pulses. But when the underlying…

Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…