In this paper, a chaos search immune algorithm (CSIA) is proposed by integrating the chaos optimization algorithm and the clonal selection algorithm. First, optimization variables are expressed by chaotic variables through solution space transformation. Then, taking advantages of the ergodic and stochastic properties of chaotic variables, a chaos search is performed in the neighbourhoods of hig...

By the penalty function methodwe transform zero-one nonlinear programming problems into unconstrained zero-one integer optimization problems. A particle swarm optimization algorithm with chaos and gene density mutation is given to solve unconstrained the zero-one nonlinear program problems. We use chaos to initialize populations and use the 0-1 integer operation in updating positions to produce...

In order to design and optimize high-linearity power amplifier (PA), which with nonlinear and memory effect, it is very important to build power amplifier behavior modeling accurately. This paper proposes a power amplifier behavior modeling based on RBF neural network with improved chaos particle swarm optimization algorithm. To make the particles evenly distribute in the problem search space, ...

The Hodgkin-Huxley model describes action potential generation in certain types of neurons and is a standard model for conductance-based, excitable cells. Following the early work of Winfree and Best, this paper explores the response of a spontaneously spiking Hodgkin-Huxley neuron model to a periodic pulsatile drive. The response as a function of drive period and amplitude is systematically ch...

In this work, we study chaos control and synchronization of the commensurate fractional order Liu system. Based on the stability theory of fractional order systems, the conditions of local stability of nonlinear three-dimensional commensurate fractional order systems are discussed. The existence and uniqueness of solutions for a class of commensurate fractional order Liu systems are investigate...

A non-vanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system, however no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ε = E/N , the energy per degree of freedom. The fu...

In piecewise-smooth dynamical systems, situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic (e.g., no periodic windows). This is the phenomenon of robust chaos. Previous works have established that robust chaos can occur through the mechanism of border-collision bifurcation, where border is the phase-space region where discontinuities ...

In this paper we present two nonlinear estimation algorithms that combine generalized polynomial chaos theory with higher moment updates and Bayesian framework. Polynomial chaos theory is used to predict the evolution of uncertainty of the nonlinear random process. In the first estimation algorithm, higher order moment updates are used to estimate the posterior non Gaussian probability density ...

xi 1 Chapter 1: Introduction 1 1.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Notation and Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Chapter 2: Asymptotic Distribution for Polynomial Chaos Representation from Data 5 2.1 Motivation and Problem Description . . . . . . . . . . . . . . . . . . . . . . ....

This paper is an expanded version of lectures given at M.S.R.I. in June of 2008. It provides an introduction to various zeta functions emphasizing zeta functions of a finite graph and connections with random matrix theory and quantum chaos. Section 2. Three Zeta Functions For the number theorist, most zeta functions are multiplicative generating functions for something like primes (or prime ide...