Hidden coexisting firings in fractional-order hyperchaotic memristor-coupled HR neural network with two heterogeneous neurons and its applications

The firing patterns of each bursting neuron are different because of the heterogeneity, which may be derived from the different parameters or external drives of the same kind of neurons, or even neurons with different functions. In this paper, the different electromagnetic effects produced by two fractional-order memristive (FOM) Hindmarsh–Rose (HR) neuron models are selected for characterizing different firing patterns of heterogeneous neurons. Meanwhile, a fractional-order memristor-coupled heterogeneous memristive HR neural network is constructed via coupling these two heterogeneous FOM HR neuron models, which has not been reported in the adjacent neuron models with memristor coupling. With the study of initial-depending bifurcation behaviors of the system, it is found that the system exhibits abundant hidden firing patterns, such as periods with different topologies, quasiperiodic firings, chaos with different topologies, and even hyperchaotic firings. Particularly, the hidden hyperchaotic firings are perfectly detected by two-dimensional Lyapunov stability graphs in the two-parameter space. Meanwhile, the hidden coexisting firing patterns of the system are excited from two scattered attraction domains, which can be confirmed from the local attraction basins. Furthermore, the color image encryption based on the system and the DNA approach owns great keyspace and a good encryption effect. Finally, the digital implementations based on Advanced RISC Machine are in good coincidence with numerical simulations.