Chaos, Its Synchronization and Anticontrol of Integral and Fractional Order Generalized Heartbeat Systems
|關鍵字:||渾沌;廣義心搏系統;范德坡系統;分數階;渾沌激發的渾沌同步;反控制;Chaos;Van deo Pol equatio;Generalized van deo Pol system;Fractional Order System;Parameter excited chaos synchronization;Anticontrol|
In this thesis, chaos of a generalized heartbeat system with integral and fractional orders is studied. Both nonautonomous and autonomous systems are considered in detail. Chaos in the nonautonomous generalized heartbeat system excited by a sinusoidal time function with integral and fractional orders is studied. Next, chaos in the autonomous generalized heartbeat system with integral and fractional orders is considered. Numerical analyses, such as phase portraits, Poincaré maps and bifurcation diagrams are observed. Chaos can be successfully obtained in the fractional order system with the total order both less than and more than the number of the states of the integral order generalized heartbeat system. Chaos excited chaos synchronizations of generalized heartbeat systems with integral and fractional order are studied. Synchronizations of two identical autonomous generalized heartbeat chaotic systems are obtained by replacing the amplitude or the sine time function of their corresponding exciting terms by the same function of chaotic states of a third nonautonomous or autonomous generalized heartbeat system, respectively. Numerical simulations, such as phase portraits, Poincaré maps and state error plots are given. Chaos excited chaos synchronizations can be successfully obtained for the fractional order systems with the total fractional order both less than and more than the number of the states of the integral order generalized heartbeat system. Anticontrol of chaos for integral and fractional order generalized nonautonomous heartbeat system is obtained effectively by adding a constant term to the system. By numerical analyses, such as phase portraits, Poincaré maps and bifurcation diagrams, anticontrol can be observed evidently.
|Appears in Collections:||Thesis|