A novel hybridization of birds of prey-based optimization with differential evolution mutation and crossover for chaotic dynamics identification

Parameter identification of chaotic systems such as Lorenz, Chen, and Rössler has long been recognized as a challenging inverse problem, since even slight perturbations in system coefficients can yield qualitatively different trajectories. Conventional time-domain error formulations are often ill-conditioned under these conditions, which has motivated the design of more robust objective functions and the adoption of metaheuristic optimization strategies. In this study, a hybrid birds of prey-based optimization with differential evolution (h-BPBODE) is introduced to address these challenges. The method enriches the four canonical behavioral phases of BPBO (individual hunting, group hunting, attacking the weakest, and relocation) by embedding DE mutation and crossover operators after each candidate update. This design injects recombinative diversity while retaining BPBO's adaptive and collective search mechanisms, thereby improving the balance between exploration and exploitation. The algorithm is validated on Lorenz, Chen, and Rössler systems, where the task is to recover unknown parameters by minimizing trajectory mismatches between true and simulated models. Comparative simulations against standard BPBO, starfish optimization, hippopotamus optimization, particle swarm optimization (PSO), and DE confirm that h-BPBODE consistently achieves exact parameter recovery with negligible residuals, faster convergence, and markedly lower run-to-run variance. Statistical analyses, convergence traces, and parameter evolution curves further demonstrate its robustness and precision. These findings establish h-BPBODE as a reliable and efficient framework for chaotic system identification and suggest its potential for broader nonlinear estimation tasks.