## Inherent Randomicity of Nonlinear Dynamical System and its Engineering Applications

- April 2, 2014
- 1 p.m.
- LeConte 312

## Abstract

In the research of nonlinear dynamical systems, we will discuss the inherent randomicity in 4-symbolic dynamics and cubic chaotic system. The symbolic sequences bear three characteristics. The distribution of inter-occurrence times and the alignment of two random sequences are amplified in detail. By using transfer probability of Markov chain (MC), we obtain analytic expressions of generating functions in four probabilities stochastic wander model, which can be applied to all 4-symbolic systems. In the fields of engineering applications, we will highlight the applications in biological engineering and electrical engineering. In the research about faults in complex electrical engineering, from the point of nonlinear dynamics, each fault in power system must correspond to one or more bifurcation locations. The power system under fault conditions should have positive Lyapunov exponent, and the actual fault location should also have the biggest Lyapunov exponent.