Estimation of the topological entropy via the direct Lyapunov method
نویسندگان
چکیده
The paper deals with the problem of estimation of the topological entropy for non-autonomous systems of differential equations via the second (direct) Lyapunov method. The main result of the paper is illustrated by examples concerning the Lorenz system and Duffing oscillator.
منابع مشابه
A topological entropy approach for observation via channels
The paper deals with the problem of estimation of the topological entropy for discrete-time nonlinear systems via the second (direct) Lyapunov method. The main result of the paper is illustrated by examples concerning the Hénon system and forced bouncing ball oscillator. An application to the observability problem via digital channels with limited data rate is discussed and the simulation resul...
متن کاملEstimation of the Entropy Rate of ErgodicMarkov Chains
In this paper an approximation for entropy rate of an ergodic Markov chain via sample path simulation is calculated. Although there is an explicit form of the entropy rate here, the exact computational method is laborious to apply. It is demonstrated that the estimated entropy rate of Markov chain via sample path not only converges to the correct entropy rate but also does it exponential...
متن کاملA New Chaotic System with Positive Topological Entropy
This paper introduces a new simple system with a butterfly chaotic attractor. This system has rich and complex dynamics. With some typical parameters, its Lyapunov dimension is greater than other known three dimensional chaotic systems. It exhibits chaotic behavior over a large range of parameters, and the divergence of flow of this system is not a constant. The dynamics of this new system are ...
متن کاملPower Swings Damping Improvement with STATCOM and SMES Based on the Direct Lyapunov Method
In this paper a comprehensive approach is presented to improve power swings damping based on direct Lyapunov method. The approach combines superconducting magnetic energy storage (SMES) system with static synchronous compensator (STATCOM). Considering the energy absorption/injection ability of SMES, in transient states the combination exchanges both active and reactive powers with power system....
متن کاملEntropy operator for continuous dynamical systems of finite topological entropy
In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.
متن کامل