Cascade chaotic neural network (CCNN): a new model

In recent years, studies on chaotic neural networks have been increased to construct a robust and flexible intelligent network resembling the human brain. To increase the chaotic performance and to reduce the time-complexity of conventional chaotic neural networks, this paper presents an innovative chaotic architecture called cascade chaotic neural network (CCNN). Cascade chaotic system is inspired by cascade structures in electronic circuits. Cascade structure is based on a combination of two or more one-dimensional chaotic maps. This combination provides a new chaotic map that has more complicated behavior than its grain maps. The fusion of this structure into the network neurons makes the CCNN more capable of confronting nonlinear problems. In the proposed model, cascade chaotic activation function (CCAF) is introduced and applied. Using the CCAF with inherent chaotic features such as increasing variability, ergodicity, maximum entropy, and free saturation zones can be promising to solve or reduce learning problems in conventional AFs without increasing complexity. The complexity does not increase because no parameter is added to the system in use. The required chaos for neural network is generated by the Li oscillator, and then when using the neural network, parameters are considered as constants. Chaotic behavior of the CCNN is investigated through bifurcation diagram. Also, prediction capability of the proposed model is verified through popular benchmark problems. Simulation and analysis demonstrate that in comparison with outstanding chaotic models, the CCNN provides more accurate and robust results in various conditions.