Extended Gauss Iterative Map: Bistability and Chimera States

We investigate an extended Gauss iterative map by incorporating the q-exponential function, a key component of the Tsallis framework. This extension enables us to investigate the non-linear dynamics of the Gauss iterative map across a broader range of scenarios, encompassing periodic, chaotic, and bistable behaviors. Regular and chaotic phenomena have been observed in coupled systems. In this context, we propose a network of coupled extended Gauss iterative maps. In our network, we found the emergence of chimera states, characterized by the coexistence of coherent and incoherent behaviors. These states are identified within specific parameter regimes using Gopal’s metric. In this work, we show the interplay between chaos and emergent collective dynamics in coupled extended Gauss iterative maps.