A Class Of Fractional Order Jerk System Control Of Chaos Synchronization And Its Application In Confidential Communication

In recent years, only the mathematics research on the fractional calculus theory, other scientists think that the theory of the fractional calculus has little value for them. But in fact, the fractional affects many natural phenomena. For example:weather and climate. The phase diagram, bifurcation diagram, chaos, chaos synchronization control of the fractional dynamical systems is the typical dynamic behavior in nonlinear field. What’s more, in this technologically advanced information age, theft has occurred frequently, confidentiality of information has aroused great attention of people in this technologically of information age, using sensitivity of fractional order chaotic systems to the characteristics of the initial parameters and the order of sensitive will achieve confidential communications on, security of the transmission of information can be enhanced greatly.Recently, the studying on Jerk system is mostly based on integer order or fractional integer model and the studying on dynamic behavior is mostly based on the phase diagram. In this paper, we studied the dynamical behavior of the integer order Jerk system and fractional order Jerk system phase diagram, the single-parameter bifurcation diagram, the two-parameter bifurcation diagram, the Poincare sections, chaos and so on; also studied the fractional Jerk synchronization control problem. And then the fractional Jerk system is applied to the confidential communications. The main contents of the paper are as follows:1. Describe the chaotic background, analysis the status of the current fractional power systems, indicate the purpose of the topics to be selected, meaning and current problems in the field; Describe the general characteristics and the judgment of the chaotic systems, Give the definition of several fractional differential method, and then describes the commonly used method of fractional chaotic system, Finally, the stability theory of fractional order chaotic systems is given.2. Study the dynamic behavior of third-order Jerk model. First, we study the equilibrium point of the integer order Jerk model; second, we take the scope of the system parameters change, study the bifurcation and chaotic phenomena and draw system fixed within the parameters of the period doubling bifurcation route to chaos; Finally, we study the dynamical behavior of the fractional Jerk model with parameters and order changing and conclude that within the parameter and order range we fixed the period doubling bifurcation leading to chaos, numerical simulation verify its effectiveness.3. Study the third-order Jerk system synchronization control. First, using a linear feedback conformity can control the chaotic system to any equilibrium point of the system by choosing the value of k. Through numerical simulation, we found that the synchronous speed is related to k. Second, tell the fractional order chaotic systems with self-synchronization and different structures, and obtained the chaos synchronization method is suitable for our system.4. Study the fractional Jerk system application in secure communication. First introduced the system of fractional Jerk confidential communication theory, the numerical simulation results verify the validity of the method, and then concluded that using the fractional order chaotic systems to maintain the confidentiality of communications, which can greatly enhance the security of the signal transmission.