Experimental Studies of Noise Effects in Nonlinear Oscillators
In the paper the noisy behavior of nonlinear oscillators is explored experimentally. Two types of excitable stochastic oscillators are considered and compared, i.e., the FitzHugh–Nagumo system and the Van der Pol oscillator with a subcritical Andronov–Hop
- PDF / 1,166,322 Bytes
- 30 Pages / 439.36 x 666.15 pts Page_size
- 23 Downloads / 210 Views
Abstract In the paper the noisy behavior of nonlinear oscillators is explored experimentally. Two types of excitable stochastic oscillators are considered and compared, i.e., the FitzHugh–Nagumo system and the Van der Pol oscillator with a subcritical Andronov–Hopf bifurcation. In the presence of noise and at certain parameter values both systems can demonstrate the same type of stochastic behavior with effects of coherence resonance and stochastic synchronization. Thus, the excitable oscillators of both types can be classified as stochastic self-sustained oscillators. Besides, the noise influence on a supercritical Andronov–Hopf bifurcation is studied. Experimentally measured joint probability distributions enable to analyze the phenomenological stochastic bifurcations corresponding to the boundary of the noisy limit cycle regime. The experimental results are supported by numerical simulations.
1 Introduction Since any real systems are subjected to random excitations, the influence of external noise on dynamical systems becomes an important research topic from both fundamental and applied viewpoints. A series of scientific monographs, among of which [1–9], and the majority of research papers are devoted to this problem.
V.S. Anishchenko • T.E. Vadivasova • A.V. Feoktistov • V.V. Semenov • G.I. Strelkova () Saratov State University, Astrakhanskaya str., 83, Saratov 410012, Russia e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected] V. Afraimovich et al. (eds.), Nonlinear Dynamics and Complexity, Nonlinear Systems and Complexity 8, DOI 10.1007/978-3-319-02353-3__10, © Springer International Publishing Switzerland 2014
261
262
V.S. Anishchenko et al.
Nonlinear dynamical systems that possess stochastic oscillations arising from random excitation (noise) can be referred to a separate class. Without external excitation, a system is in its stable equilibrium state. Such systems are called stochastic oscillators and demonstrate the number of fundamental effects, such as stochastic resonance (SR) [10–13], coherence resonance (CR) [14, 15], and stochastic synchronization (SS) [12, 13, 16–18]. At certain conditions nonlinear stochastic oscillators possess some features of self-sustained oscillatory systems. This fact enables to call these systems as stochastic self-sustained oscillators [19]. One of the fundamental properties of self-sustained oscillations that can demonstrate stochastic self-sustained oscillators is their ability to synchronization. As noted above, this feature is also inherent in bistable stochastic oscillators [13, 16, 17] and excitable oscillators [13, 20–22]. Additionally, stochastic synchronization for excitable systems is completely similar to synchronization of a noisy self-sustained oscillator. This analogy is related with the fact that the spectrum of stochastic oscillations of excitable systems exhibits a peak at a certain characteristic nonzero frequency, which is sufficiently narrow in the CR regime. The effect of coheren
Data Loading...
