Various dynamics of a ring of non-identical attention deficit disorder maps

Various regimes of a ring of non-identical attention deficit disorder (ADD) models are studied in this paper. The ADD model used in this paper can show multistability. The dynamics of the coupled maps are investigated by changing the coupling strength and parameter mismatch. In this study, a similarity function is used for the lag synchronization analysis of the coupled maps. To explore the dynamics, state space, bifurcation diagram, and largest Lyapunov exponent are analyzed. By investigating the control parameters of the map, different bifurcations, including a transition from periodic dynamics to quasiperiodic and chaotic behavior, transition from chaotic to periodic and periodic to chaotic attractors are observed. The results show exciting dynamics in the ring of non-identical ADD maps. However, proper lag synchronization is not observed in the chaotic regions; the periodic and quasiperiodic areas demonstrate an appealing lag synchronization. Furthermore, the ring of non-identical ADD maps can illustrate multistability similar to the uncoupled ADD model.