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In this paper, a boost converter emulator with a memristive load instead of a resistive load is proposed, and a fractional-order model of the memristive boost converter is created. Firstly, the fractional-order models of the memristor and the memristive boost converter are established respectively, and then based on different switching states, the circuit equations of the fractional-order memristive boost converter operating in continuous conduction mode are derived. Secondly, the dynamic characteristics of the fractional-order system are analyzed by numerical simulations and are compared with the integer-order memristive boost converter. Furthermore, the effects of the memristive load on the system is studied by comparing it to the traditional boost converter with resistive load. The results indicate that the fractional-order memristive boost converter can exhibit rich dynamic behavior by adjusting bifurcation parameters, and the fractional-order circuit system expands the stable working regions of the integer-order circuit system. Meanwhile, the addition of the memristive load significantly widens the normal working regions. Finally, simulations of the fractional-order system circuit based on PSIM further verify the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we consider the evolution of an ensemble of noninteracting classical particles confined in a closed region. Each one of these particles experiences several elastic collisions with a rigid-smooth oval-like boundary. As known in the literature, numerical simulations for this kind of system demand too much time, mostly because of the time spent in solving transcendental equations. To deal with that, we highlight an alternative approach to speed up the search of solutions for the transcendental equations via the tangent method, which has proved to be a faster way to solve this problem when compared with other methods, like the bisection one. The methods applied here are generic and can be used or adapted for other billiard boundaries. [ABSTRACT FROM AUTHOR]

We report on a stripe-core mixed spiral chimera in a system of nonlocally coupled phase oscillators, located on the spherical surface, where the spiral wave consisting of phase-locked oscillators is separated by a stripe-type region of incoherent oscillators into two parts. We analyze the existence and stability of the stripe-core mixed spiral chimera state rigorously, on the basis of the Ott–Antonsen reduction theory. The stability diagram for the stationary states including the spiral chimeras as well as incoherent state is presented. Our stability analysis reveals that the stripe-core mixed spiral chimera state emerges as a unique attractor and loses its stability via the Hopf bifurcation. We verify our theoretical results using direct numerical simulations of the model system. [ABSTRACT FROM AUTHOR]