Dynamics of chaotic system based on circuit design with Ulam stability through fractal-fractional derivative with power law kernel

In this paper, the newly developed Fractal-Fractional derivative with power law kernel is used to analyse the dynamics of chaotic system based on a circuit design. The problem is modelled in terms of classical order nonlinear, coupled ordinary differential equations which is then generalized through Fractal-Fractional derivative with power law kernel. Furthermore, several theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. The highly non-linear fractal-fractional order system is then analyzed through a numerical technique using the MATLAB software. The graphical solutions are portrayed in two dimensional graphs and three dimensional phase portraits and explained in detail in the discussion section while some concluding remarks have been drawn from the current study. It is worth noting that fractal-fractional differential operators can fastly converge the dynamics of chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.

Automated summary

In this paper, the dynamics of a chaotic system based on a circuit design is analyzed using the newly developed Fractal-Fractional derivative with power law kernel. The problem is modeled using classical order nonlinear, coupled ordinary differential equations, which are then generalized through Fractal-Fractional derivative with power law kernel. The theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. A numerical technique using MATLAB software is used to analyze the highly non-linear fractal-fractional order system. The graphical solutions are presented in two dimensional graphs and three dimensional phase portraits and discussed in detail, with some concluding remarks drawn from the study. It is worth noting that fractal-fractional differential operators can quickly converge the dynamics of a chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.