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In this paper, Chua’s circuit model with a fractional-order memristor is proposed and investigated from the viewpoint of nonlinear dynamics. Unlike the previous fractional-order models as generalizations of integer-order memristive Chua’s circuit in the literature, by replacing all the first-order derivatives in the system equation with fractional-order derivatives, the proposed model has only one fractional-order derivative in the system equation, introduced on the basis of a physical observation. Stability and bifurcation are analyzed for a sub-system, and numerical simulation is done for the whole circuit system. “Intermittent chaos” resulting from tangent bifurcation or grazing bifurcation is found numerically, for which limit cycle and chaotic attractor switch with very high frequency. This is a typical feature of nonsmooth dynamic systems, and the nonsmoothness is caused mainly by the fractional-order derivative. [ABSTRACT FROM AUTHOR]

For the stability analysis of time-delay systems, the available methods usually require the exact evaluation of some quantities. The definite integral stability method, originated from the Argument Principle or the Cauchy Theorem, is effective because it only requires a rough estimation of the testing integral over a finite interval to judge stability. However, no general rule is given in the literature for properly choosing the upper limit of the testing integral. In this paper, two simple algorithms are presented for finding the parameter-dependent critical upper limit and a parameter-independent upper limit without any restriction on the number of time delays. These results improve and complete the definite integral stability method. As illustrated by the numerical examples, the proposed algorithms work effectively and accurately. [ABSTRACT FROM AUTHOR]