Leaderless synchronization of heterogeneous oscillators by adaptively learning the group model

International audienc

Adaptive Synchronization of Complex Dynamical Networks with State Predictor

This paper addresses the adaptive synchronization of complex dynamical networks with nonlinear dynamics. Based on the Lyapunov method, it is shown that the network can synchronize to the synchronous state by introducing local adaptive strategy to the coupling strengths. Moreover, it is also proved that the convergence speed of complex dynamical networks can be increased via designing a state predictor. Finally, some numerical simulations are worked out to illustrate the analytical results

Synchronization of heterogeneous harmonic oscillators for generalized uniformly jointly connected networks

The synchronization problem for heterogeneous harmonic oscillators is investigated. In practice, the communication network among oscillators might suffer from equipment failures or malicious attacks. The connection may switch extremely frequently without dwell time, and can thus be described by generalized uniformly jointly connected networks. We show that the presented typical control law is strongly robust against various unreliable communications. Combined with the virtual output approach and generalized Krasovskii-LaSalle theorem, the stability is proved with the help of its cascaded structure. Numerical examples are presented to show the correctness of the control law

Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis

We show how the Equation-Free approach for multi-scale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of simulated annealing we compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level. We also exploit the scheme to perform a rare-events analysis by estimating an effective Fokker-Planck describing the evolving probability density function of the corresponding coarse-grained observables