Abstract
In this paper, we present a corresponding fractional order three-dimensional autonomous chaotic system based on a new class of integer order chaotic systems. We found that the fractional order chaotic system belongs to the generalized Lorenz system family by analyzing its linear term and topological structure. We also found that the equilibrium point generated by the fractional order system belongs to the unstable saddle point through the prediction correction method and the fractional order stability theory. The complexity of fractional order chaotic system is given by spectral entropy algorithm andC0algorithm. We concluded that the fractional order chaotic system has a higher complexity. The fractional order system can generate rich dynamic behavior phenomenon with the values of the parameters and the order changed. We applied the finite time stability theory to design the finite time synchronous controller between drive system and corresponding system. The numerical simulations demonstrate that the controller provides fast and efficient method in the synchronization process.
Highlights
Chaos, as a standout in the field of nonlinearity, has shown great vitality over the past five decades since Lorenz introduced a continuous three-dimensional autonomous system from the meteorological problems and studied it as the first chaotic model [1]
We present a corresponding fractional order three-dimensional autonomous chaotic system based on a new class of integer order chaotic systems
We found that the fractional order chaotic system belongs to the generalized Lorenz system family by analyzing its linear term and topological structure
Summary
As a standout in the field of nonlinearity, has shown great vitality over the past five decades since Lorenz introduced a continuous three-dimensional autonomous system from the meteorological problems and studied it as the first chaotic model [1]. Scholars have done more research on chaotic systems through explaining the integer order mathematical models [12,13,14]. (i) Many physical systems reveal fractional dynamic behavior due to their special feature; it is more common to study the fractional calculus models to explain the fractional order system. The fractional order chaotic system can be synchronously controlled in a finite time by certain conditions. It has important research value for the application technology in practical engineering fields, especially in the field of secure communication, which can realize more complex dynamic behavior and improve the overall security of the communication system.
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