Chaotic systems without equilibrium points represent a significant class of nonlinear dynamical systems because their behavior cannot be interpreted through conventional equilibrium-based analysis. In this study, a novel four-dimensional fractional-order chaotic system without equilibrium points is proposed and analyzed.

The results reveal bistable dynamics characterized by the coexistence of two distinct attractors under the same parameter set and different initial conditions, including symmetric limit cycles and chaotic attractors with different geometric structures. These dynamical features are exploited to enhance trajectory unpredictability in autonomous mobile robotic applications. Furthermore, a fixed-time synchronization framework is developed for large-scale multi-agent systems. In contrast to conventional asymptotic methods, the proposed strategy ensures convergence within a prescribed time bound independent of the initial states. The framework is then implemented in a masterslave robotic swarm, linking fractional-order reference dynamics with integer-order kinematic agents. Numerical investigations confirm the capability of the proposed method to achieve accurate synchronization and reliable trajectory tracking in networked robotic systems.