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Chaotic synchronization with gap junction of multi-neurons in external electrical stimulation. (English) Zbl 1091.34027
Consider a coupled system of the form $$ \dot u_j = f(u_j,t)+C\sum_{i=1,i\ne j}^n (u_i-u_j), \quad j=1,2,\dots $$ The authors give sufficient conditions for complete synchronization, i.e., stability of the invariant subspace $u_1=u_2=\cdots=u_n$. Here, $C$ is the coupling matrix and the uncoupled dynamics is described by the following forced oscillator $$ \frac{dX}{dt} = X(X-1)(1-rX)-Y+I_0(t), \quad \frac{dY}{dt} = bX, $$ with some parameters $r$, $b$, and periodic force $I_0(t)$.

MSC:
34D05Asymptotic stability of ODE
34C60Qualitative investigation and simulation of models (ODE)
34C15Nonlinear oscillations, coupled oscillators (ODE)
34C30Manifolds of solutions of ODE (MSC2000)
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References:
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