Finite-time synchronization of fractional-order chaotic system based on hidden attractors

A new 3D fractional-order chaotic system is obtained by improving the Sprott-A system and introducing the definition of fractional calculus to it. Then the new system is certified to be chaotic by studying and analyzing the phase diagram, Lyapunov exponents, and smaller alignment index tests. Then the analysis of equilibrium points finds that the new system has virtually no equilibrium points and hidden attractors. The new system is dynamically analyzed by bifurcation diagram, time-domain waveform and complexity, it is indicated that the system is susceptible to initial conditions, and with the changes of different parameters the system produced different scroll types of attractors. In addition, to verify the feasibility of the system, a simulation circuit design based on Multisim is therefore carried out. Finally, the finite-time synchronization of the fractional-order system is successfully achieved by taking advantage of the high security of the hidden attractors.

Automated summary

By improving the Sprott-A system and introducing the definition of fractional calculus, a new 3D fractional-order chaotic system is obtained. The system's chaotic behavior is confirmed through phase diagram, Lyapunov exponents, and alignment index tests, while its equilibrium points and dynamics are analyzed.