Finite-time outer synchronization between two complex dynamical networks with time delay and noise perturbation
TL;DR: Finite-time stochastic outer synchronization and generalized outer synchronization between two complex dynamic networks with time delay and noise perturbation with sufficient conditions for the finite-time outer synchronization are obtained.
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Abstract: In this paper, the finite-time stochastic outer synchronization and generalized outer synchronization between two complex dynamic networks with time delay and noise perturbation are studied. Based on the finite-time stability theory, sufficient conditions for the finite-time outer synchronization are obtained. Numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of time delay and noise perturbation on the convergence time are also numerically demonstrated.
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Figures
Fig. 4. (a) Time evolution of total synchronization error E(t) with time delay σ = 1.0, 2.0, 3.0 and τ = 4; (b) The corresponding logarithmic plot. 
Fig. 3. (a) Time evolution of total synchronization error E(t) with time delay τ = 1, 2, 4, 8 and σ = 0.3; (b) The corresponding logarithmic plot. 
Fig. 1. Chaotic attractor generated by the system (27) when α = 0.03, β = 1.5, γ = 0.2, µ = 1.5, ε = 0.75, ρ = 21.43 and δ = 0.075. 
Fig. 2. Trajectories of synchronization error (a) and the total synchronization error (b) between network (1) and (2) with k = 3, λ = 1.5, θ = 0.6, σ0 = 1, τ = 0.3. 
Fig. 6. The trajectory of first node x1j(j = 1, 2, 3) of Rössler-like system and the first node y1j(j = 1, 2, 3) of Lorenz system. 
Fig. 7. Trajectories of synchronization error (a) and the total synchronization error (b) between networks (1) and (2) with σ0 = 1.5, τ = 1, p = 0.5..
Citations
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