Global multistability and analog circuit implementation of an adapting synapse-based neuron model
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ORIGINAL PAPER
Global multistability and analog circuit implementation of an adapting synapse-based neuron model Bocheng Bao . Yongxin Zhu . Chengqing Li . Han Bao . Quan Xu
Received: 13 May 2020 / Accepted: 18 July 2020 Springer Nature B.V. 2020
Abstract Generally, neural networks involve the change with time of the neuron activities and that in strength of the synapses between neurons. This paper investigates the global multistability and analog circuit implementation of a two-dimensional adapting synapse-based neuron model in depth. The neuron model is non-autonomous and possesses periodically switchable equilibrium states associated with the externally imposed input closely. In every full periodic cycle of the input, the equilibrium stability has complex dynamical transitions between stable and unstable points via Hopf/fold bifurcations, resulting in the emergence of the global multistability that was not yet reported previously. Complex dynamics of the global coexisting multiple firing activities are demonstrated by multiple numerical measures, such as bifurcation plot, dynamical map, phase plane plot, and basin of attraction. Furthermore, an off-the-shelf discrete component-based circuit design is optimized to implement the neuron model and the outputs agree with the numerical results well.
B. Bao Y. Zhu H. Bao Q. Xu (&) School of Information Science and Engineering, Changzhou University, Changzhou 213164, China e-mail: [email protected] C. Li College of Computer Science and Electronics Engineering, Hunan University, Changsha 410082, China
Keywords Circuit implementation Firing activity Multistability Neuron model Switchable equilibrium
1 Introduction Dynamic processes in neural networks can be classified as two types: the change with time of the neuron activity and the change in strength of the synapses among neurons [1]. Once the neural networks start learning or evolving, both the dynamic processes occur simultaneously and their dynamical activities interact. Thus, a reasonable model conceived for the neural network is often composed of two sets of nonlinear ordinary differential equations: one describes neuron activity, and another one specifies synapse dynamics [2, 3]. In short, the adapting synapse-based neuron model in [1] can achieve the combination of synapses and activities, which was applied to the problem of the development of synaptic connections in the visual cortex. Afterward, the shortterm memory trace was demonstrated in the local and rapidly adapting synapses of inferior temporal cortex [4]. Recently, a model for neural learning was developed [5] and then the spatial features of synaptic adaptation affecting learning performance were investigated in detail.
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In the last few decades, some neuron firing activities were disclosed via numerous mathematical neuron models [6–8]. By imitating the physiological neuromodulation of a single neuron, an effective approach to enable control of a neuromorphic circuit
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