2026, Vol.29, No.1, pp.57 - 68

In this work, we explore the possibility of chimera states in the locally coupled q-deformed Lozi maps. The deformation is introduced using the Jaganathan-Sinha q-deformation scheme, which modifies the local map while smoothly recovering the standard Lozi map in the limit q →1 . We observe that the q-deformed map exhibits significant modifications in its dynamical behavior compared to the standard case. Through analytical considerations and numerical simulations, we analyze fixed points, stability, bifurcation structure, and routes to chaos as functions of the deformation parameter. Chimera states are represented by stable coexisting synchronous and asynchronous domains in a lattice of coupled identical oscillators promoted by non-local or global coupling. An analogous ``spatial intermittency'' is also observed in coupled map lattices. This work demonstrates that chimera states are not restricted to oscillatory systems or standard maps, but can also emerge in discrete-time systems with rationally deformed dynamics under purely local interactions. This indicates that chimera states are a robust and generic feature of a wide class of non-linear systems.

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