Dynamics editing of the Hopfield neural network

Every neuron exhibits diverse dynamics for its biological function. The transitions among these modes are typically challenging, which normally resorts to parameter adjustment. As a result, it is limited in terms of real-time performance and reproducibility, thereby affecting functional switching in neuronal systems. In this work, the free dynamics editing is obtained based on the observation of system evolution. By introducing a piecewise-linear (PWL) feedback function, the typical oscillations of the neuron are collected and integrated into the same phase space for the free extraction of neuron dynamics. All these selected dynamics dwell in the corresponding basins of attraction and can be invoked through the initial conditions, which yields an editable, arbitrarily accessible, and reproducible oscillation library. The basins of attraction and the editing thresholds are interdependent, all of which are associated with the editing PWL function characterized by segments and slopes. Based on the Euler discretization scheme, all the edited dynamics are implemented on the FPGA platform by means of resource reuse and initial condition switching.