We consider the effect of external noise on the dynamics of limit cycle oscillators. The Lyapunov exponent becomes negative under influence of small white noise, what means synchronization of two or more identical systems subject to common noise. We analytically study the effect of small non-identities in the oscillators and in the noise, and derive statistical characteristics of deviations fro...

The paper contains technical details and proofs of recent results developed by the author, regarding the design of LPV controllers directly from experimental data. A numerical example is also presented, about control of the Duffing oscillator.

We derive the exact bifurcation diagram of the Duffing oscillator with parametric noise thanks to the analytical study of the associated Lyapunov exponent. When the fixed point is unstable for the underlying deterministic dynamics, we show that the system undergoes a noise-induced reentrant transition in a given range of parameters. The fixed point is stabilised when the amplitude of the noise ...

Cryptography and steganography are among the most important sciences that have been properly used to keep confidential data from potential spies hackers. They can be separately or together. Encryption involves basic principle of instantaneous conversion valuable information into a specific form unauthorized persons will not understand decrypt it. While is science embedding inside cover, in way ...

We establish necessary and sufficient conditions for the solvability of nonlinear boundary-value problem in critical case develop a scheme construction solutions this problem. By using Newton–Kantorovich method, we propose new iterative determination to weakly system ordinary differential equations case. As examples application constructed scheme, obtain approximations periodic Duffing Lienard ...