Dynamical Analysis of a Caputo Fractional-Order Modified Brusselator Model: Stability, Chaos, and 0-1 Test

Differential equations have demonstrated significant practical effectiveness across diverse fields, including physics, chemistry, biological engineering, computer science, electrical power systems, and security cryptography. This study investigates the dynamics of a Caputo fractional discrete-time modified Brusselator model. Conditions for the existence and local stability of the fixed point FP are established. Using bifurcation theory, the occurrence of both period-doubling and Neimark–-Sacker bifurcations is analyzed, revealing that these bifurcations occur at specific values of the bifurcation parameter. Maximum Lyapunov characteristic exponents are computed to assess system sensitivity. Two-dimensional diagrams are presented to illustrate phase portraits, local stability regions, closed invariant curves, bifurcation types, and Lyapunov exponents, while the 0-1 test confirms the presence of chaos in the model. Finally, MATLAB simulations validate the theoretical results.