Analysis of the Noise-Induced Regimes in Ricker Population Model with Allee Effect via Confidence Domains Technique

We consider a discrete-time Ricker population model with the Allee effect under the random disturbances. It is shown that noise can cause various dynamic regimes, such as stable stochastic oscillations around the equilibrium, noise-induced extinction, and a stochastic trigger. For the parametric analysis of these regimes, we develop a method based on the investigation of the dispersions and arrangement of confidence domains. Using this method, we estimate threshold values of the noise generating such regimes

Controlling the Stochastic Sensitivity in Nonlinear Discrete-Time Systems with Incomplete Information

For stochastic nonlinear discrete-time system with incomplete information, a problem of the stabilization of equilibrium is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations

Analysis of noise-induced transitions from regular to chaotic oscillations in the Chen system

The stochastically perturbed Chen system is studied within the parameter region which permits both regular and chaotic oscillations. As noise intensity increases and passes some threshold value, noise-induced hopping between close portions of the stochastic cycle can be observed. Through these transitions, the stochastic cycle is deformed to be a stochastic attractor that looks like chaotic. In this paper for investigation of these transitions, a constructive method based on the stochastic sensitivity function technique with confidence ellipses is suggested and discussed in detail. Analyzing a mutual arrangement of these ellipses, we estimate the threshold noise intensity corresponding to chaotization of the stochastic attractor. Capabilities of this geometric method for detailed analysis of the noise-induced hopping which generates chaos are demonstrated on the stochastic Chen system. © 2012 American Institute of Physics

On the Regulators with Random Noises in Dynamic Block

The problem of controlling stochastic linear systems with quadratic criterion is considered. A class of optimal controllers which are equivalent to the separation theorem regulator is determined. For all of such controllers the quadratic functional has the same value. The effects of disregarded disturbances which are modeled by random noises in the dynamic block of the regulator are investigated. It is shown that the equivalent (in the classic propounding) controllers respond to these noises in different ways. Sometimes an "equivalent optimal" regulator may be less receptive towards additional disturbances than the standard one (which comes from the separation theorem). The optimal regulator is found which takes into account the presence of such noises

Stochastic Analysis of Subcritical Amplification of Magnetic Energy in a Turbulent Dynamo

We present and analyze a simplified stochastic $\alpha \Omega -$dynamo model which is designed to assess the influence of additive and multiplicative noises, non-normality of dynamo equation, and nonlinearity of the $\alpha -$% effect and turbulent diffusivity, on the generation of a large-scale magnetic field in the subcritical case. Our model incorporates random fluctuations in the $\alpha -$parameter and additive noise arising from the small-scale fluctuations of magnetic and turbulent velocity fields. We show that the noise effects along with non-normality can lead to the stochastic amplification of the magnetic field even in the subcritical case. The criteria for the stochastic instability during the early kinematic stage are established and the critical value for the intensity of multiplicative noise due to $\alpha -$fluctuations is found. We obtain numerical solutions of non-linear stochastic differential equations and find the series of phase transitions induced by random fluctuations in the $\alpha -$parameter.Comment: 21pages,7 figure