140 research outputs found
Breaking an image encryption algorithm based on chaos
Recently, a chaos-based image encryption algorithm called MCKBA (Modified
Chaotic-Key Based Algorithm) was proposed. This paper analyzes the security of
MCKBA and finds that it can be broken with a differential attack, which
requires only four chosen plain-images. Performance of the attack is verified
by experimental results. In addition, some defects of MCKBA, including
insensitivity with respect to changes of plain-image/secret key, are reported.Comment: 10 pages, 4 figure
Stochastic Analysis and Control in Kinetics of Multistable Chemical Reactor
We consider a model of thermochemical reactor proposed by Nowakowski. Stochastic effects in the bistability zone are studied. A parametric analysis of noise-induced transitions between coexisting equilibria is carried out on the basis of the stochastic sensitivity technique and confidence ellipses method. We solve the problem of stabilization of the equilibrium regime under incomplete information. The feedback regulator which reduces the stochastic sensitivity and stabilizes the randomly forced equilibrium is constructed. © 201
Dynamics of a ring of three unidirectionally coupled Duffing oscillators with time-dependent damping
We study dynamics of a ring of three unidirectionally coupled double-well
Duffing oscillators for three different values of the damping coefficient:
fixed dumping, proportional to time, and inversely proportional to time. The
dynamics in all cases is analyzed through time series, Fourier and Hilbert
transforms, Poincar\'e sections, as well as bifurcation diagrams and Lyapunov
exponents with respect to the coupling strength. In the first case, we observe
a well-known route from a stable steady state to hyperchaos through Hopf
bifurcation and a series of torus bifurcations, as the coupling strength is
increased. In the second case, the system is highly dissipative and converges
into one of stable equilibria. Finally, in the third case, transient toroidal
hyperchaos takes place
Multistability and stochastic phenomena in a randomly forced thermochemical system
A model of the thermochemical reactor with well mixing is considered. An impact of random noise on the attractors of this model is studied in zones of saddle-node bifurcations with transitions from mono- to bimodal dynamics. Phenomena of the stochastic excitability and noise-induced transitions are demonstrated. Critical values of the noise intensities corresponding to the onset of generation of the large-amplitude stochastic oscillations are estimated
Multistability and stochastic dynamics of Rulkov neurons coupled via a chemical synapse
We study complex dynamics of two Rulkov neurons unidirectionally connected via a chemical synapse with respect to three control parameters: (i) a parameter responsible for the type of dynamical behavior of a solitary neuron, (ii) coupling strength, and (iii) noise intensity. The coupled system exhibits various scenarios on the route from a stable equilibrium to chaos with respect to the coupling strength. We observe a variety of dynamical regimes, including mono-, bi- and tri-stability, order-chaos transitions and vice versa, as well as the coexistence of in-phase and anti-phase synchronization. We also study transitions between in-phase and out-of-phase synchronization with statistics on the duration of synchronization intervals and transitions from order to chaos. In addition to numerical simulations, we demonstrate the effectiveness of the analytical confidence ellipses method based on stochastic sensitivity approach. © 2023 The Author(s)Russian Science Foundation, RSF: 21-11-00062The work was supported by the Russian Science Foundation (project No. 21-11-00062)
Stochastic phenomena in pattern formation for distributed nonlinear systems
We study a stochastic spatially extended population model with diffusion, where we find the coexistence of multiple non-homogeneous spatial structures in the areas of Turing instability. Transient processes of pattern generation are studied in detail. We also investigate the influence of random perturbations on the pattern formation. Scenarios of noise-induced pattern generation and stochastic transformations are studied using numerical simulations and modality analysis. © 2020 The Author(s) Published by the Royal Society. All rights reserved.Russian Science Foundation, RSF: 16-11-10098Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally. Competing interests. We declare we have no competing interests. Funding. The work was supported by the Russian Science Foundation (grant no. 16-11-10098)
Autonomous Bursting in a Homoclinic System
A continuous train of irregularly spaced spikes, peculiar of homoclinic
chaos, transforms into clusters of regularly spaced spikes, with quiescent
periods in between (bursting regime), by feeding back a low frequency portion
of the dynamical output. Such autonomous bursting results to be extremely
robust against noise; we provide experimental evidence of it in a CO2 laser
with feedback. The phenomen here presented display qualitative analogies with
bursting phenomena in neurons.Comment: Submitted to Phys. Rev. Lett., 14 pages, 5 figure
Detecting specific oscillatory regimes in the dynamics of erbium-doped fiber laser
A method for determining the oscillatory mode occurring in an erbiumdoped fiber laser with a modulated parameter is proposed. The method is based on using a continuous wavelet transform with a mother Morlet wavelet and analyzing the energy of the wavelet spectrum that corresponds to the relevant range of time scales
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Statistical Properties and Predictability of Extreme Epileptic Events
The use of extreme events theory for the analysis of spontaneous epileptic brain activity is a relevant multidisciplinary problem. It allows deeper understanding of pathological brain functioning and unraveling mechanisms underlying the epileptic seizure emergence along with its predictability. The latter is a desired goal in epileptology which might open the way for new therapies to control and prevent epileptic attacks. With this goal in mind, we applied the extreme event theory for studying statistical properties of electroencephalographic (EEG) recordings of WAG/Rij rats with genetic predisposition to absence epilepsy. Our approach allowed us to reveal extreme events inherent in this pathological spiking activity, highly pronounced in a particular frequency range. The return interval analysis showed that the epileptic seizures exhibit a highly-structural behavior during the active phase of the spiking activity. Obtained results evidenced a possibility for early (up to 7 s) prediction of epileptic seizures based on consideration of EEG statistical properties
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