Dynamics analysis and FPGA implementation of discrete memristive cellular neural network with heterogeneous activation functions

The activation function, as an important component of artificial neural networks, endows neural networks with rich dynamical phenomena by virtue of its nonlinear properties. However, especially for cellular neural networks (CNNs), the exploration of neural networks consisting of heterogeneous activation functions has not been sufficient. In this article, we introduce heterogeneous activation functions in discrete cellular neural network (DCNN) for the first time. In order to enhance the dynamics of the original DCNN, we propose our discrete memristive cellular neural network (DMCNN) based on a memristor with a sinusoidal function. Using various methods of dynamical characterization, such as Lyapunov exponential analysis, bifurcation diagrams and spectral entropy, the rich dynamical behaviour of the proposed model is comprehensively investigated, including hyperchaos, transient chaos, high spectral entropy and multiple types of coexisting attractors in the proposed model. Last but not least, the hardware platform of the proposed model is implemented by field programmable gate array (FPGA), and the dynamics of the proposed model is verified by a combination of software simulation and hardware experiments. The new exploration of DMCNN with heterogeneous activation functions in this article lays the foundation for further research into neural networks with complex dynamical behaviour.