Related papers: Local sensitivity of spatiotemporal structures
We study the reliability of spike output in a general class of pulse-coupled oscillators receiving a fluctuating input. Showing that this problem is equivalent to noise-induced synchronization between identical networks of oscillators, we…
We study the influence of telegraph noise on synchrony of limit cycle oscillators. Adopting the phase description for these oscillators, we derive the explicit expression for the Lyapunov exponent. We show that either for weak noise or…
We study numerically synchronization phenomena of spatiotemporal structures, including chimera states, in a two layer network of nonlocally coupled nonlinear chaotic discrete-time systems. Each of the interacting ensembles represents a one…
We report the occurrence of a self-emerging frequency chimera state in spatially extended systems of coupled oscillators, where the coherence and incoherence are defined with respect to the emergent frequency of the oscillations. This is…
We demonstrate that a system of nonlocally coupled noisy phase oscillators can collectively exhibit a hole structure, which manifests itself in the spatial phase distribution of the oscillators. The phase model is described by a nonlinear…
The transient stability of power systems and synchronization of non-uniform Kuramoto oscillators are closely related problems. In this paper, we develop a novel regional stability analysis framework based on the proposed region-parametrized…
We investigate the behavior of the Lyapunov spectrum of a linear discrete-time system under the action of small perturbations in order to obtain some verifiable conditions for stability and openness of the Lyapunov spectrum. To this end we…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be…
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…
We present simple classical dynamical models to illustrate the idea of introducing a stochasticity with non-locality into the time variable. For stochasticity in time, these models include noise in the time variable but not in the "space"…
We study cluster synchronization in networks and show that the stability of all possible cluster synchronization patterns depends on a small set of Lyapunov exponents. Our approach can be applied to clusters corresponding to both orbital…
We discuss Hamiltonian model of oscillator lattice with local coupling. Model describes spatial modes of nonlinear Schr\"{o}dinger equation with periodic tilted potential. The Hamiltonian system manifests reversibility of Topaj - Pikovsky…
Nonlocally coupled oscillator systems can exhibit an exotic spatiotemporal structure called chimera, where the system splits into two groups of oscillators with sharp boundaries, one of which is phase-locked and the other is…
We consider small network models for mutually delay-coupled systems which typically do not exhibit stable isochronally synchronized solutions. We show that for certain coupling architectures which involve delayed self feedback to the nodes,…
Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing…
We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate…
Spatial structure can arise in spatial point process models via a range of mechanisms, including neighbour-dependent directionally biased movement. This spatial structure is neglected by mean-field models, but can have important effects on…
The threshold, or saturation phenomenon of spatially coupled systems is revisited in the light of Lyapunov's theory of dynamical systems. It is shown that an application of Lyapunov's direct method can be used to quantitatively describe the…
In distributed-parameter inverse problems in computational mechanics, spatially varying fields are inferred from noisy, indirect, and heterogeneous observations. The relevant identifiability question concerns which spatial perturbation…