Coupling schemes for cluster synchronization in coupled Josephson equations. (English) Zbl 1066.34046

Qin, Wen-Xin; Chen, Guanrong

Physica D 197, No. 3-4, 375-391 (2004).

The paper considers the system of coupled Josephson equations \[ \Phi'' + \alpha \Phi + \beta A \Phi + f(\Phi) =I, \] where \(\Phi=(\phi_1,\phi_2,\dots,\phi_n)^T\), the damping coefficient \(\alpha>0\), the constant input \(I=(I_1,I_2,\dots,\) \(I_n)^T \in \mathbb{R}^n\), \(f(\Phi) =(\sin(\phi_1),\sin(\phi_2),\dots,\sin(\phi_n))^T\). \(\beta>0\) measures the coupling strength and \(A\) is a real matrix reflecting the coupling topology.
The authors propose an approach for constructing such coupling schemes, i.e., the matrix \(A\), that a selected cluster synchronization pattern is stable. In particular, a coupling scheme is given to create a synchronization with the frequency ratio \(m_1:m_2:\cdots:m_n\).

Reviewer: Sergiy Yanchuk (Berlin)

MSC:

34D05	Asymptotic properties of solutions to ordinary differential equations
34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C30	Manifolds of solutions of ODE (MSC2000)
34C60	Qualitative investigation and simulation of ordinary differential equation models

Keywords:

cluster synchronization; coupling scheme; Josephson equations

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