Dynamic Analysis And Synchronization Of Fractional-order Chaotic System With Hidden Attractors

Since Lorenz found the first chaotic attractor in the atmospheric convection model in 1963,and the research focus has gradually changed from how to avoid chaos at the beginning to the effective use of chaos.It has been proved that the properties of chaotic signal,such as unpredictability,high complexity and continuous broadband spectrum,are very suitable for secure communication.The fractional-order chaotic system and hyperchaotic system all have more complicated dynamical behaviors than the integer one.However,most of the researches on chaotic system at home and abroad are still based on the integer order,there is little research on the fractional-order chaotic systems.Based on the above problems,a series of researches have been carried out around the hidden fractional-order chaotic system in this paper.The specific work can be divided into the following two parts:(1)Based on the classical integral order chaotic system,a new fractional-order chaotic system with hidden attractors is constructed.The complex dynamical behaviors of this new fractional-order chaotic system are studied by nonlinear research tools such as phase diagram,bifurcation diagram,Lyapunov exponent spectrum,complexity spectrum and so on.Many special dynamics are found,including bursting oscillations,coexistence of attractors,offset boosting,multistability and others.Then,based on the improved modular design idea and the mathematical model of the fractional-order chaotic system,the chaotic circuit is designed by the basic unit circuit consisting of operational amplifier.Finally,the chaotic circuit is realized on both the circuit simulation platform and the hardware experiment platform,various attractors are captured successfully,and the circuit experiment results are consistent with the numerical simulation results.(2)The complicated dynamical behaviors of the fractional-order hyperchaotic Li's system are studied by nonlinear research tools.In addition to the multistability caused by different initial values,attractor type mutation caused by the introduction of offset boosting is also found.Few fractional-order chaotic systems can show the existence of different types of attractors caused by two different reasons,especially the fractional-order chaotic system with hidden attractors.The corresponding synchronization circuit is designed and realized by using one-way coupling synchronization method,which fully proves the effectiveness of the synchronization method.To further verify the physical realizability of the system,the hardware circuit of the fractional-order hyperchaotic system constructed by basic electronic components is implemented on a breadboard,and the hyperchaotic attractors are successfully captured on oscilloscope.