A New Mega-Stable System with a Mosaic Pattern and Its Hamilton Energy Analysis

Scientists have been interested in designing and analyzing new dynamical systems with desirable characteristics in recent decades. Such systems can be used to study a wide range of complex phenomena. This study presents the design of a new two-dimensional mega-stable nonlinear system, which is highly sensitive to initial conditions. Depending on these initial conditions, the system can exhibit an infinite number of coexisting limit cycles. Several of these attractors are self-excited, as their basins contain a fixed point, while many others are hidden. These trajectories form a mosaic pattern in the phase space. The system also possesses numerous equilibria, with some being stable and many others unstable. In addition to a comprehensive investigation of this mega-stable system, its forced version is also explored. By applying a periodic force, the system’s dynamics become more complex. Depending on the amplitude of the force term, the system’s attractor can exhibit a toroidal, chaotic, or periodic behavior. The Hamilton energy of the mega-stable system is also investigated. It demonstrates how the energy drops as the system’s frequency increases.