Chaotic behavior is a common feature of nonlinear dynamics, as well as
The subject of our discussion today is to study the stability of hyperchaos in high-dimensional systems. This study serves as an introductory guide to a discrete fractional four-dimensional hyperchaotic Rössler system with a Caputo-like operator, which is a complex system that can be used to study chaos in discrete fractional nonlinear dynamics. Our results demonstrate the existence of a hyperchaotic invariant set in these systems, leading to extended hyperchaotic transient behavior. The coexistence of chaos and hyperchaos is evident in the numerical results, which are presented as phase plots and bifurcation diagrams for various fractional orders and different parameters and initial conditions. These diagrams provide a comprehensive explanation of the dynamics of the proposed discrete system. This research substantiates the presence of chaos in discrete fractional hyperchaotic Rössler systems that are reminiscent of Caputo-like discrete systems. Control low is offered to display synchronization of coupled Caputo-like discrete fractional hyperchaotic Rössler systems and to force the states of the proposed system to converge asymptotically to zero. The findings of the study are demonstrated through the following numerical simulations, which have been a significant development in our research.