Lev B. Ryashko

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We study excitability phenomena for the stochastically forced FitzHugh-Nagumo system modeling a neural activity. Noise-induced changes in the dynamics of this model can be explained by the high stochastic sensitivity of its attractors. Computational methods based on the stochastic sensitivity functions technique are suggested for the analysis of these(More)
We study the stochastically forced Lorenz model in the parameter zone admitting two coexisting limit cycles under the transition to chaos via period-doubling bifurcations. Noise-induced transitions between both different parts of the single attractor and two coexisting separate attractors are demonstrated. The effects of structural stabilization and noise(More)
We present a new computer approach to the spatial analysis of stochastically forced 3D-cycles in nonlinear dynamic systems. This approach is based on a stochastic sensitivity analysis and uses the construction of confidence tori. A confidence torus as a simple 3D-model of the stochastic cycle adequately describes its main probabilistic features. We suggest(More)
The limit cycles of nonlinear systems under the small stochastic disturbances are considered. The random trajec-tories of forced system leave the deterministic cycle and form some stochastic bundle around it. The probabilistic description of this bundle near cycle based on stochastic sensitivity function (SSF) is suggested. The SSF is a covariance matrix(More)
We present and analyze a simplified stochastic αΩ−dynamo model which is designed to assess the influence of additive and multiplicative noises, non-normality of dynamo equation, and nonlinearity of the α−effect and turbulent diffusivity, on the generation of a large-scale magnetic field in the subcritical case. Our model incorporates random fluctuations in(More)
The effects of stochastic perturbations on a non-normal dynamical system mimicking a laminar-to-turbulent subcritical transition are investigated both analytically and numerically. It is found that a nonlinear dynamical system with non-normal transient linear growth is very sensitive to the presence of weak random perturbations. The effect of non-normality(More)
Fast convergence of the Coiflet-Galerkin method for general elliptic BVPs Hani Akbari Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils Tadeusz Kaczorek A multivariable multiobjective predictive controller Stability of softly switched multiregional dynamic output controllers with a(More)
We study a stochastically forced predator-prey model with Allee effect. In the deterministic case, this model exhibits non-trivial stable equilibrium or limit cycle corresponding to the coexistence of both species. Computational methods based on the stochastic sensitivity functions technique are suggested for the analysis of the dispersion of random states(More)