1,132 research outputs found
Stochastic resonance with different periodic forces in overdamped two coupled anharmonic oscillators
We study the stochastic resonance phenomenon in the overdamped two coupled
anharmonic oscillators with Gaussian noise and driven by different external
periodic forces. We consider (i) sine, (ii) square, (iii) symmetric saw-tooth,
(iv) asymmetric saw-tooth, (v) modulus of sine and (vi) rectified sinusoidal
forces. The external periodic forces and Gaussian noise term are added to one
of the two state variables of the system. The effect of each force is studied
separately. In the absence of noise term, when the amplitude of the applied
periodic force is varied cross-well motion is realized above a critical value
() of . This is found for all the forces except the modulus
of sine and rectified sinusoidal forces.Stochastic resonance is observed in the
presence of noise and periodic forces. The effect of different forces is
compared. The logarithmic plot of mean residence time
against where is the intensity of the noise and
is the value of at which cross-well motion is initiated
shows a sharp knee-like structure for all the forces. Signal-to-noise ratio is
found to be maximum at the noise intensity at which mean
residence time is half of the period of the driving force for the forces such
as sine, square, symmetric saw-tooth and asymmetric saw-tooth waves. With
modulus of sine wave and rectified sine wave, the peaks at a value of
for which sum of in two wells of the potential of the system is
half of the period of the driving force. For the chosen values of and
, signal-to-noise ratio is found to be maximum for square wave while it
is minimum for modulus of sine and rectified sinusoidal waves.Comment: 13 figures,27 page
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
Networks of coupled oscillators: From phase to amplitude chimeras
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 28, 113124 (2018) and may be found at https://doi.org/10.1063/1.5054181.We show that amplitude-mediated phase chimeras and amplitude chimeras can occur in the same network of nonlocally coupled identical oscillators. These are two different partial synchronization patterns, where spatially coherent domains coexist with incoherent domains and coherence/incoherence referring to both amplitude and phase or only the amplitude of the oscillators, respectively. By changing the coupling strength, the two types of chimera patterns can be induced. We find numerically that the amplitude chimeras are not short-living transients but can have a long lifetime. Also, we observe variants of the amplitude chimeras with quasiperiodic temporal oscillations. We provide a qualitative explanation of the observed phenomena in the light of symmetry breaking bifurcation scenarios. We believe that this study will shed light on the connection between two disparate chimera states having different symmetry-breaking properties.
Chimera states are emergent dynamical patterns in networks of coupled oscillators where coherent and incoherent domains coexist due to spontaneous symmetry-breaking. In oscillators that exhibit both phase and amplitude dynamics, two types of distinct chimera patterns exist, namely, amplitude-mediated phase chimeras (AMCs) and amplitude chimeras (ACs). In the AMC state coherent and incoherent regions are distinguished by different mean phase velocities: all coherent oscillators have the same phase velocity, however, the incoherent oscillators have disparate phase velocities. In contrast to AMC, in the AC state, all the oscillators have the same phase velocity, however, the oscillators in the incoherent domain show periodic oscillations with randomly shifted center of mass. Surprisingly, in all the previous studies on chimeras, a given network of continuous-time dynamical systems seems to show either AMC or AC: they never occur in the same network. In this paper, for the first time, we identify a network of coupled oscillators where both AMC and AC are observed in the same system, and we also provide a qualitative explanation of the observation based on symmetry-breaking bifurcations.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept
On the complex dynamics of intracellular ganglion cell light responses in the cat retina
We recorded intracellular responses from cat retinal ganglion cells to sinusoidal flickering lights and compared the response dynamics to a theoretical model based on coupled nonlinear oscillators. Flicker responses for several different spot sizes were separated in a 'smooth' generator (G) potential and eorresponding spike trains. We have previously shown that the G-potential reveals complex, stimulus dependent, oscillatory behavior in response to sinusoidally flickering lights. Such behavior could be simulated by a modified van der Pol oscillator. In this paper, we extend the model to account for spike generation as well, by including extended Hodgkin-Huxley equations describing local membrane properties.
We quantified spike responses by several parameters describing the mean and standard deviation of spike burst duration, timing (phase shift) of bursts, and the number of spikes in a burst. The dependence of these response parameters on stimulus frequency and spot size could be reproduced in great detail by coupling the van der Pol oscillator, and Hodgkin-Huxley equations. The model mimics many experimentally observed response patterns, including non-phase-locked irregular oscillations. Our findings suggest that the information in the ganglion cell spike train reflects both intraretinal processing, simulated by the van der Pol oscillator) and local membrane properties described by Hodgkin-Huxley equations. The interplay between these complex processes can be simulated by changing the coupling coefficients between the two oscillators. Our simulations therefore show that irregularities in spike trains, which normally are considered to be noise, may be interpreted as complex oscillations that might earry information.Whitehall Foundation (S93-24
Random Delays and the Synchronization of Chaotic Maps
We investigate the dynamics of an array of logistic maps coupled with random
delay times. We report that for adequate coupling strength the array is able to
synchronize, in spite of the random delays. Specifically, we find that the
synchronized state is a homogeneous steady-state, where the chaotic dynamics of
the individual maps is suppressed. This differs drastically from the
synchronization with instantaneous and fixed-delay coupling, as in those cases
the dynamics is chaotic. Also in contrast with the instantaneous and
fixed-delay cases, the synchronization does not dependent on the connection
topology, depends only on the average number of links per node. We find a
scaling law that relates the distance to synchronization with the randomness of
the delays. We also carry out a statistical linear stability analysis that
confirms the numerical results and provides a better understanding of the
nontrivial roles of random delayed interactions.Comment: 5 pages, 5 figure
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