Simulation of Continuous Markov Processes in Discrete-Time for Signals Described by Stochastic Differential Equations

We considered the issues associated with methods for solving the problems of representation of continuous Markov processes in discrete-time by the example of radar signals, which are subject to the simultaneous effect of additive and multiplicative noise described by stochastic differential equations. We considered the algorithm, which allows us to carry out computer simulation of fading amplitude, phase and information parameter of the signal in discrete observation time using the example of a continuous frequency-modulated signal, the amplitude of which adheres to the Nakagami distribution that is typical for radar signals under simultaneous effect of additive and multiplicative noise. It is shown that with the help of computer simulation it is possible to create not only optimal algorithms, but also their corresponding optimal structural diagrams, which makes it possible to elevate the processing of radar signals to higher standards.

Stochastic dynamic behavior of FitzHugh–Nagumo neurons stimulated by white noise

Stochastic noise exists widely in the nervous system, and noise plays an extremely important role in the information processing of the nervous system. Noise can enhance the ability of neurons to process information as well as decrease it. For the dynamic behavior of stochastic resonance and coherent resonance shown by neurons under the action of stochastic noise, this paper uses Fourier coefficient and coherence resonance coefficient to measure the behavior of stochastic resonance and coherence resonance, respectively, and some conclusions are drawn by analyzing the effects of additive noise and multiplicative noise. Appropriate noise can make the nonlinear system exhibit stochastic resonance behavior and enhance the detection ability of external signals. It can also make the coherent resonance behavior of the nonlinear system reach its optimal state, and the system becomes more orderly. By comparing the effects of additive and multiplicative noise on the stochastic resonance behavior and coherent resonance behavior of the system, it is found that additive and multiplicative noise can both make the system appear the phenomenon of stochastic resonance and have almost identical discharge state at the same noise intensity. However, with the increase of noise intensity, the coherent resonance of the system occurs, the multiplicative noise intensity is smaller than that of additive noise, but the coherent resonance coefficient of additive noise is smaller and the coherent resonance effect is better. The system whose system parameters are located near the bifurcation point is more prone to coherent resonance, and the closer the bifurcation point is, the more obvious the coherent resonance phenomenon is, and the more regular the system becomes. When the parameters of the system are far away from the bifurcation point, the coherent resonance will hardly appear. Besides, when additive and multiplicative noise interact together, the stochastic resonance and coherent resonance phenomena are more likely to appear at small noise, and the behavior of stochastic resonance and coherent resonance that the system shown is better in the local range.

Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

Non-Gaussian additive and multiplicative noise-induced chaos in the lateral vibration of a viscoelastic plate: A fully analytic approach

In this study, the chaotic behavior of a viscoelastic plate under integrated non-Gaussian additive and multiplicative bounded noise is investigated with an analytical approach. First, the governing equation of motion of the system was derived by introducing a set of dimensionless parameters. After that, the modified version of Melinkov’s function in terms of statistical indices was obtained, and then, for a spectrum of bounded noises, the boarder curves of chaotic areas were obtained. The model of sine/cosine Wiener was chosen for the bounded noise which enables the researcher to produce a range of wide and narrowband noises. For the case that the excitation is only additive, or only multiplicative, and that both excitations exist simultaneously, the effect of variations in structural properties and noise characteristics on the chaos area were investigated. It was shown that at frequencies close to the natural frequency of the corresponding linear system, narrowband excitations affected the chaotic behavior more than the wideband ones and vice versa. To validate the results, a numerical simulation was also made.