Chaotic Particle Optimization, Chaos Anticontrol And Its Application In Encryption

The real world is nonlinear. If human beings want to investigate the nature more clearly, it is necessary to study the complicated nonlinear system. Chaos, which is a deterministic system with random behaviors, exists in the world and is one of the important research fields of nonlinear systems. With the continual endeavor for the past forty years, chaos theory has obtained lots of substantial results and already been applied in some fields such as communication and information process.The paper introduces the development of chaos at first. Then based on the knowledge of chaotic system, a new chaos particle swarm algorithm and a chaos antification of fractiaonal order method are proposed. At last, we apply the fractional chaotic system in the encryption, and then verify the validity of this method via simulations. The main works are as follows:1. The single particle structure of particle swarm optimization is analyzed. It has some properties of chaotic Hopfield neural network. A new particle model is proposed. Its search procedure is not in a stochastic way as the original particle model but in a deterministically invert bifurcation structure. This structure convergence can be analyzed easily. This paper gives the system convergence result. Finally, the numerical simulation is provided to show the use procedure and its efficiency.2. It is found that the Lorenz system with integer order is in stable or periodic state in some parameter scope; however it can produce chaos with fractional order less than 1, which is demonstrated by bifurcation diagram and phase portraits. The numerical simulations demonstrate the tendency that the fractional order increases bigger, the Lorenz system is more unstable.3. The chaotic time series is produced by applying the fractional system, and then apply the chaos to the encryption. The fundamental principle of encryption algorithm is firstly analyzed, and then a kind of encryption approach based on fractional order chaos is proposed. This approach has low computational load and is easy to implement.