Related papers: Robust Almost Global Splay State Stabilization of …
The stability of the dynamical states characterized by a uniform firing rate ({\it splay states}) is analyzed in a network of globally coupled leaky integrate-and-fire neurons. This is done by reducing the set of differential equations to a…
We propose an encoding and control strategy for the stabilization of switched systems with limited information, supposing the controller is given for each mode. Only the quantized output and the active mode of the plant at each sampling…
We study the synchronisation properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronise from the stability of this behaviour. While…
The collective behavior of biological oscillators has been recognized as an important problem for several decades, but its control has come into limelight only recently. Much of the focus for control has been on desynchronization of an…
We investigate phase synchronization between two identical or detuned response oscillators coupled to a slightly different drive oscillator. Our result is that phase synchronization can occur between response oscillators when they are…
We study synchronization in delay-coupled oscillator networks, using a master stability function approach. Within a generic model of Stuart-Landau oscillators (normal form of super- or subcritical Hopf bifurcation) we derive analytical…
We prove a converse Lyapunov theorem for almost sure stabilizability and almost sure asymptotic stabilizability of controlled diffusions: given a stochastic system a.s. stochastic open loop stabilizable at the origin, we construct a lower…
We present an approach for reconstructing networks of pulse-coupled neuron-like oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases…
In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum of Squares optimisation. Particularly, we use Sum of Squares optimisation to search for a Lyapunov function that…
We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled…
We study singularly perturbed systems that exhibit input-to-state stability (ISS) with fixed-time properties in the presence of bounded disturbances. In these systems, solutions converge to the origin within a time frame independent of…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
In this study, we propose new global stabilization approaches for a class of polynomial systems in both model-based and data-driven settings. The existing model-based approach guarantees global asymptotic stability of the closed-loop system…
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…
We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions---subsets of the phase space filled…
Synchronization of coupled oscillators is a ubiquitous phenomenon found throughout nature. Its robust realization is crucial to our understanding of various nonlinear systems, ranging from biological functions to electrical engineering. On…
Networks of coupled phase oscillators play an important role in the analysis of emergent collective phenomena. In this article, we introduce generalized $m$-splay states constituting a special subclass of phase-locked states with vanishing…
Understanding complex systems which exhibit desynchronization as an emergent property should have important implications, particularly in treating neurological disorders and designing efficient communication networks. Here were demonstrate…
In this paper, we extend well-known relationships between global asymptotic controllability, sample stabilizability, and the existence of a control Lyapunov function to a wide class of control systems with unbounded controls, which includes…
We show that a large class of pulse coupled oscillators converge with high probability from random initial conditions on a large class of graphs with time delays. Our analysis combines previous local convergence results, probabilistic…