Abstract

This paper explores a novel fractional-order modification of the Rössler system via the Caputo differential operator. The dynamical system is augmented to a four-dimensions space by appending a four-state variable, thereby increasing the dynamical complexity of the new system and enabling it to produce hyperchaotic dynamics. A sinusoidal function is additionally included within the governing equations, giving rise to novel class of nonlinear dynamical interaction compared to the original Rossler system. The equilibrium states of the fractional-order system (1) are computed, and the stability behavior in the vicinity of these points is explored through the use of the linearization matrix coupled with the well-known Matignon’s stability criterion. The system analytically shown to be dissipative, which establishes the fact that its trajectories are bounded with the evolution of time. The dynamical characteristic of system (1) is examined via computational simulations using FDE12 method, the Adams-Bash fourth-Moulton predictor-corrector algorithm. The obtained results confirm the existence of distinct dynamical regimes, including chaotic and hyperchaotic attractors. These results are affirmed by means of the Lyapunov exponents and strengthened through the 0–1 diagnostic test for chaos. The impact of varying the system parameters is also highlighted through bifurcation diagram. To apply system (1) to recorded real data, the governing parameters are determined via genetic algorithm based on EEG recordings, retrieved from the PhysioNet open-access database. Signals from the Fz, Cz, Pz channels and parietal midline Wz are used. The comparison between simulated and real data shows similar dynamical patterns, indicating that the model can capture important features of neural activity. Overall, the proposed system (1) provides a useful framework for studying complex nonlinear dynamics and may be applied in the analysis of biological signals.