Bifurcation control of a fractional-order chaotic laser system with multi-scale memory and dual time delays

We establish a fractional-order chaotic laser model with multi-scale memory and analyze its Hopf bifurcation, further designing a dual time-delay fractional-order controller for active dynamical regulation. The proposed model introduces a multi-scale memory architecture with three independent fractional orders \(q_1,q_2,q_3∈(0,1]\), individually assigned to picosecond optical field coherence, nanosecond carrier recombination, and microsecond thermal diffusion, coupled with cubic susceptibility and Gaussian gain saturation to enable fine-tuned control of stability and bifurcation. A dual time-delay fractional-order proportional-derivative controller is designed, combining instantaneous state feedback with distributed memory compensation, enabling flexible switching among equilibrium, periodic, and chaotic regimes by suppressing or exciting Hopf bifurcation on demand. Numerical simulations validate the theoretical predictions, demonstrating precise bifurcation control and robust chaos suppression. These findings establish a foundation for memory-aware photonic engineering with applications in secure optical communication and physical random number generation.