2,306 research outputs found

    Pulsive feedback control for stabilizing unstable periodic orbits in a nonlinear oscillator with a non-symmetric potential

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    We examine a strange chaotic attractor and its unstable periodic orbits in case of one degree of freedom nonlinear oscillator with non symmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a pulsive feedback technique. Discrete set of pulses enable us to transfer the system from one periodic state to another.Comment: 11 pages, 4 figure

    On the validity of memristor modeling in the neural network literature

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    An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks

    Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses

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    Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a theory to predict the stationary distribution of pairwise phase difference from the phase response curve, which quantitatively encapsulates the oscillator dynamics, via averaging of the Frobenius-Perron equation describing the impulse-driven oscillators. The validity of our theory is confirmed by direct numerical simulations using the FitzHugh-Nagumo neural oscillator receiving common Poisson impulses as an example

    Phase reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems

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    Reaction-diffusion systems can describe a wide class of rhythmic spatiotemporal patterns observed in chemical and biological systems, such as circulating pulses on a ring, oscillating spots, target waves, and rotating spirals. These rhythmic dynamics can be considered limit cycles of reaction-diffusion systems. However, the conventional phase-reduction theory, which provides a simple unified framework for analyzing synchronization properties of limit-cycle oscillators subjected to weak forcing, has mostly been restricted to low-dimensional dynamical systems. Here, we develop a phase-reduction theory for stable limit-cycle solutions of infinite-dimensional reaction-diffusion systems. By generalizing the notion of isochrons to functional space, the phase sensitivity function - a fundamental quantity for phase reduction - is derived. For illustration, several rhythmic dynamics of the FitzHugh-Nagumo model of excitable media are considered. Nontrivial phase response properties and synchronization dynamics are revealed, reflecting their complex spatiotemporal organization. Our theory will provide a general basis for the analysis and control of spatiotemporal rhythms in various reaction-diffusion systems.Comment: 19 pages, 6 figures, see the journal for a full versio

    Dynamics of delay induced composite multi-scroll attractor and its application in encryption

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    This work was supported in part by NSFC (60804040, 61172070), Key Program of Nature Science Foundation of Shaanxi Province (2016ZDJC-01), Innovative Research Team of Shaanxi Province(2013KCT-04), Fok Ying Tong Education Foundation Young Teacher Foundation(111065), Chao Bai was supported by Excellent Ph.D. research fund (310-252071603) at XAUT.Peer reviewedPostprin
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