TURK 2025

Chaos theory and its possible applications have attracted an increasing number of academics over the last forty years, particularly from the mathematical, physical, and engineering disciplines. Specifically, there has been a recent uptick in the interest in studying 4D chaotic systems that include both hidden and coexisting attractor types. In this study, we captured the system's non-locality by generalizing the standard 4D chaotic model with the non-local impact. The system's well-posedness has been verified by studying its boundedness. Furthermore, the stability analysis confirms that the system is unstable. More specifically, we show how to use Lyapunov exponents and bifurcation parameter analysis to determine the optimal range for a system's level of chaos. Using Picard's operator, we investigated the existence and uniqueness of the solutions and showed that the system under consideration had two unstable equilibrium points. The system's chaotic behavior is depicted in figures that demonstrate the presence of two-wing attractors, four-wing attractors, and coexisting attractors, as the considered model is nonlinear. Fractional Euler's method is employed for the numerical simulations and a specific set of parameters.