2,306 research outputs found
Pulsive feedback control for stabilizing unstable periodic orbits in a nonlinear oscillator with a non-symmetric potential
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
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
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
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
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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