| Popis: |
In this work, a design of a constant and time-varying fractional Newton-Lepnick system is developed to understand its chaotic properties. Due to the nonlocal nature of the method, the Newton-Leipnik system is generated using a generalized power law, a power law and another fractional derivative based on the Mittag-Leffler function developed as a kernel. We solve the model using the numerical Caputo-Fabiesu method, but also test their existence and uniqueness. These schemes are applied to oscillators of chaotic Newton-Lepnic systems based on simulated chaotic circuits. Chaos control is performed by a linear controller. Furthermore, the Lyapunov exponent of the system indicates that the chaos control results are correct. We demonstrate the applicability and effectiveness of this method with a numerical example. Numerical simulation of the controller is provided. 2010 Mathematics Subject Classification. 92D30, 92D25, 92C42, 34C60. |
