In large-scale high-density integrated circuits, memristors in close proximity to one another both influence, and are influenced by, the behavior of nearby memristors. However, the previous analyses of memristors-based circuit applications have seldom considered the possibility of coupling effects between memristors which invariably influences the response of all memristors, thus rendering much previous research as incomplete. In this paper, the circuit dynamics of memristive Chua's circuits are systematically analyzed based on a pair of compositely connected flux-controlled memristors characterized by cubic nonlinearity as a typical example. A theoretical analysis is undertaken and verified via MATLAB. While tuning the coupling strength, variations in circuit dynamics are characterized by phase portraits, bifurcation diagrams, and Lyapunov exponents. A new floating memristor emulator with coupling ports, described by cubic nonlinearity, is designed using off-the-shelf circuit devices and is shown to be successfully used in building chaotic circuits in hardware experiments, verifying theoretical results in simulations. This paper provides a new way through which memristors-based circuit dynamics can be influenced by tuning the coupling strength between memristors without changing other circuit parameters. It is further highlighted that when designing future memristors-based circuits, the coupling action between memristors should be considered if necessary and compensated when causing undesired circuit responses.
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