A Note on Chaos in Hayward Black Holes with String Fluids

Abstract

In this work, we first examine the onset of thermodynamic chaos in Hayward AdS black holes with string fluids, emphasizing the effects of temporal and spatially periodic perturbations. We apply Melnikov's approach to examine the perturbed Hamiltonian dynamics and detect the onset of chaotic behavior. In the case of temporal perturbations induced by thermal quenches, chaos occurs for perturbation amplitude $\gamma$ exceeding a critical threshold, determined by charge $q$ and the string fluid parameter. From the equation of state of the black hole, a general condition is established indicating that under temporal perturbations, the existence of charge is an essential prerequisite for chaos. However, regardless of the presence of charge, spatial perturbations result in chaotic behavior. Further next, we compute the Lyapunov exponent associated with the thermodynamic system to further quantify chaotic behavior beyond the threshold condition. We demonstrate that the string fluid density and the Hayward regularization parameter have a considerable effect on the amplitude of the Lyapunov exponent, showing the control of thermal instability by regular geometry corrections and matter sources. These results highlight the rich nonlinear dynamics arising from the interplay of geometric regularization, matter content, and phase-space instability.