Related papers: Dynamical behaviours in time-delay systems with de…
We study the interplay between network topology and complex space-time patterns and introduce a concept to analytically predict complex patterns in networks of Stuart-Landau oscillators with linear symmetric and instantaneous coupling based…
We discuss applications of time-delayed feedback control to delay-coupled neural systems and lasers, in the framework of the FitzHugh-Nagumo neuron model and the Lang-Kobayashi laser model, respectively. In the context of neural systems, we…
The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic…
We investigate heterogeneous coupling delays in complex networks of excitable elements described by the FitzHugh-Nagumo model. The effects of discrete as well as of uni- and bimodal continuous distributions are studied with a focus on…
The dynamics of one-way coupled systems with discrete time is considered. The behavior of the coupled logistic maps is compared to the dynamics of maps obtained using the Poincare sectioning procedure applied to the coupled continuous-time…
We study the nonlinear dynamics of two delay-coupled neural systems each modelled by excitable dynamics of FitzHugh-Nagumo type and demonstrate that bistability between the stable fixed point and limit cycle oscillations occurs for…
Coupled limit cycle oscillators with pairwise interactions depict phase transitions to amplitude or oscillation death. This Letter introduces a scheme for higher-order interactions, which can not be decomposed into pairwise interactions. We…
Time-delay systems are, in many ways, a natural set of dynamical systems for natural scientists to study because they form an interface between abstract mathematics and data. However, they are complicated because past states must be…
Here we extend a recent review (Physics Reports {\bf 521}, 205 (2012)) of amplitude death, namely the suppression of oscillations due to the coupling interactions between nonlinear dynamical systems. This is an important emergent phenomenon…
Multiplex networks provide a proper framework for understanding the dynamics of complex systems with differing types of interactions. This study considers different dynamical states possible in a multiplex network of nonlinear oscillators,…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
A general scheme for construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the…
Unidirectionally coupled area-preserving maps with a mixed phase space may show identical synchronization in the sticky neighborhood of the regular islands. We use this fact to devise numerical procedures to control (delay and expedite) the…
We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…
The dynamics of coupled 2D chaotic maps with time-delay on a scalefree-tree is studied, with different types of the collective behaviors already been reported for various values of coupling strength [1]. In this work we focus on the…
We study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength ($\varepsilon$), range of the interaction ($\alpha$), that can vary from first-neighbors to…
We explore and experimentally demonstrate the phenomena of amplitude death (AD) and the corresponding transitions through synchronized states that lead to AD in coupled {\it intrinsic time-delayed} hyperchaotic oscillators interacting…
Feedback delay has been identified as a key ingredient in the quorum sensing synchronization of synthetic gene oscillators. While this influence has been evidenced at the theoretical level in a simplified system of degrade-and-fire…