Related papers: Dynamic link switching induces stable synchronized…
A sufficiently connected topology linking the constituent units of a complex system is usually seen as a prerequisite for the emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phase…
We discuss the synchronization of coupled neurons which are modelled as FitzHugh-Nagumo systems. As smallest entity in a larger network, we focus on two diffusively coupled subsystems, which can be interpreted as two mutually interacting…
Complex networks are a successful framework to describe collective behaviour in many applications, but a notable gap remains in the current literature, that of proving asymptotic convergence in networks of piecewise-smooth systems. Indeed,…
Time-varying connections are crucial in understanding the structures and dynamics of complex networks. In this paper, we propose a continuous-time switching topology model for temporal networks that is driven by bursty behavior and study…
We investigate the combined effects of distributed delay and the balance between excitatory and inhibitory nodes on the stability of synchronous oscillations in a network of coupled Stuart--Landau oscillators. To this end a network model is…
This paper deals with stabilization of discrete-time switched linear systems when explicit knowledge of the state-space models of their subsystems is not available. Given the set of admissible switches between the subsystems, the admissible…
Synaptic, dendritic and single-cell kinetics generate significant time delays that shape the dynamics of large networks of spiking neurons. Previous work has shown that such effective delays can be taken into account with a rate model…
We propose a methodology to analyze synchronization in an ensemble of diffusively coupled multistable systems. First, we study how two bidirectionally coupled multistable oscillators synchronize and demonstrate the high complexity of the…
It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [G\'omez-Garde\~nes \emph{et al.} Phys.Rev.Letts. 106, 128701 (2011)] and chaotic oscillators [Leyva \emph{et al.}…
We analyze synchronization of relaxation oscillations in multiple-timescale reaction-diffusion systems. Interpreting synchronization as convergence to frequency-synchronized wave-train solutions, we resolve for the first time the case of…
We investigate the synchronization dynamics of two coupled noise-driven FitzHugh-Nagumo systems, representing two neural populations. For certain choices of the noise intensities and coupling strength, we find cooperative stochastic…
Inter-layer synchronization is a distinctive process of multiplex networks whereby each node in a given layer undergoes a synchronous evolution with all its replicas in other layers, irrespective of whether or not it is synchronized with…
We examine traveling-wave solutions on a regular ring network with one additional long-range link that spans a distance d. The nodes obey the FitzHugh-Nagumo kinetics in the excitable regime. The additional shortcut induces a plethora of…
Most previous studies on coupled dynamical systems assume that all interactions between oscillators take place uniformly in time, but in reality, this does not necessarily reflect the usual scenario. The heterogeneity in the timings of such…
The three-dimensional (3D) Fitzhugh-Nagumo neuron model with inertia was shown to exhibit a chaotic mixed-mode dynamics composed of large-amplitude spikes separated by an irregular number of small-amplitude chaotic oscillations. In contrast…
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…
Oscillatory synchrony is hypothesized to support the flow of information between brain regions, with different phase-locked configurations enabling activation of different effective interactions. Along these lines, past work has proposed…
In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple ``rhythms''…
Diverse complex systems often undergo sudden changes in their states, such as epileptic seizures, climate changes, and social uprisings. Such behavior has been modeled by noise-induced escape of bistable elements, which is the escape from…
We show that simultaneous synchronization between two delay-coupled oscillators can be achieved by relaying the dynamics via a third mediating element, which surprisingly lags behind the synchronized outer elements. The zero-lag…