Dynamics of the Dadras-Momeni System in the Frame of the Caputo-Fabrizio Fractional Derivative
Investigation of chaos in dynamical systems is one of the most fascinating issues that has received a lot of attention across a variety of scientific domains. One such dynamical system which generates two, three, and four-scroll chaotic attractors with a single parameter change, is the novel Dadras-Momeni system. In this study, we have analyzed the Dadras-Momeni system in the frame of the Caputo-Fabrizio fractional derivative. Theoretical aspects such as boundedness, existence, and uniqueness of solutions are presented. A detailed analysis is presented regarding the stability of points of equilibrium. To regulate chaos in this fractional-order system with unpredictable dynamics, a sliding mode controller is developed and the global stability of the system with control law is established. Later, we introduced uncertainties and external disturbances to the controlled system, and the condition of global stability is derived. To perform numerical simulation we have identified certain values of the parameters where the system exhibits chaotic behavior. Then the theoretical claims about the influence of the controller on the system are established with the help of numerical simulations. 2023 Taylor & Francis Group, LLC.
Special Functions in Fractional Calculus and Engineering, pp. 241-269.
https://doi.org/10.1201/9781003368069-11 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85163493507&doi=10.1201%2f9781003368069-11&partnerID=40&md5=d6e0fc9e2c89e0e5bce099fa35ac378c
Baishya C., Department of Studies and Research in Mathematics, Tumkur University, Tumkur, India; Veeresha P., Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India