Lev B. Ryashko

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Proliferation and migration dichotomy of the tumor cell invasion is examined within two non-Markovian models. We consider the tumor spheroid, which consists of the tumor core with a high density of cells and the outer invasive zone. We distinguish two different regions of the outer invasive zone and develop models for both zones. In model I we analyze the(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)
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 trajectories 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 for(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)
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)
We study the stochastically forced Chen system in its parameter zone under the transition to chaos via period-doubling bifurcations. We suggest a stochastic sensitivity function technique for the analysis of stochastic cycles. We show that this approach allows to construct the dispersion ellipses of random trajectories for any Poincaré sections, and these(More)