Modified Genesio-Tesi systems with trigonometric functions and the Caputo fractional derivative

Abstract

The new fractional-order Genesio-Tesi system is introduced, and its boundedness, stability of the equilibrium points, Lyapunov stability, uniqueness of the solution, and bifurcation are all discussed in this paper. Using the efficient predictor-corrector approach, we statistically analyze the Genesio-Tesi system in fractional order. The results effectively conceptualize and visualize the novel fractional order Genesio-Tesi systems that are suggested. When the system's order shifts from integer to fractional, the revolution around the fixed point increases.

The chaotic character of the modified Genesio-Tesi system is comparable to that of the original Genesio system. The major changes were made to the Geensio-Tesi system by including the trigonometric functions, keeping the initial conditions and parameter values intact. The system is fractionalised with the help of Caputo fractional operator. In particular, the modified system's nature is more complex, which may aid in signal processing and secure communication. Future research on the modified Genesio-Tesi system can now proceed in light of this finding. This article offers a fresh approach to utilizing and thoroughly researching the Genesio-Tesi systems that have been provided.