Neuromorphic dynamics and behavior synchronization of fractional-order memristive synapses

Abstract

Neuromorphic computing has garnered significant attention for its ability to emulate biological neural networks, yet challenges remain in simulating the behavioral dynamics and constructing the structural frameworks of neural synapses. This paper examines the neuromorphic dynamics and synchronization of fractional-order memristive systems, highlighting their potential as artificial synapses in neuromorphic computing. A 3-D fractional-order circuit was developed based on mathematical modeling of locally active memristors, revealing diverse neurodynamic behaviors, including action potentials, oscillations, and spike bursting, under varying fractional-order indices and parameters. The fractional-order boundaries for neuromorphic behaviors were discussed, and dynamic variations across different initial conditions were analyzed. A fractional-order finite-time synchronization controller was designed to achieve effective behavioral synchronization between independent memristive synapses. These findings offer valuable insights into the dynamic complexity of fractional-order systems, paving the way for their application in the design of neuromorphic systems and artificial neural networks.