Dynamical analysis of the M-ℂomplex Lorenz system and its anti-synchronization via M-Sliding mode control

Abstract

This work deals with a numerical analysis of a Complex Lorenz system generalized by the truncated M-derivative (M-ℂLM). First, we carry out 10000 random simulations based on the Monte Carlo principle and the 0–1 test with the chaos decision tree to show that, on average, the M-ℂLM depicts chaotic dynamics because its growth rate is 0.9611±0.0183. Next, we offer that M-ℂLM has two positive Lyapunov exponents, which implies hyper-chaos presence. Later, we display that the M-ℂLM holds its sensitivity to initial conditions. We use the numerical results to establish an anti-synchronization scheme via a sliding mode control using the truncated M-derivative. We reach the control objective because the response system follows the drive system even when the first does not have dynamics in the imaginary part. Finally, the anti-synchronization of two identical M-ℂLM is implemented on the Arduino Leonardo board using classical techniques to solve non-integer first-order differential equations. Based on their acquired states through the serial port, we conclude that the floating-point numbers on this board do not influence to reach the control purpose. Those above could be an excellent alternative for developing proposals involving low-cost devices with the truncated M-derivative.

Keywords

• M-complex Lorenz model
• Truncated M-derivative
• M-Sliding mode control