Abstract
A nonlinear circuit is proposed which a memristor is coupled with Josephson Junction to trigger chaotic oscillation, and the dynamics is investigated. Based on the Kirchhoff's theorem, the circuit equations are approached and then the dimensionless dynamical equations are presented after scale transformation. A regular network with nearest neighbor connection is bridged to investigate the stability and transition of spatial pattern by applying currents with diversity on the network. Coherence function, signal to noise ratio (SNR) and synchronization factor are defined to estimate the statistical properties and dynamical stability. A variety of beautiful patterns are developed by setting appropriate gradient forcing and noise intensity.
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