Abstract
In this paper, a new type of non-volatile locally active memristor with bi-stability is proposed by injecting appropriate voltage pulses to realize a switching mechanism between two stable states. It is found that the memristive parameters of the new memristor can affect the local activity, which has been rarely reported, and this phenomenon is explained based on mathematical analyses and numerical simulations. Then, a locally active memristive coupled neuron model is constructed using the proposed memristor as a connecting synapse. The parameter-associated dynamical behaviors are revealed by bifurcation plots, phase plane portraits and dynamical evolution maps. Moreover, the bi-stability phenomenon of the new coupled neuron model is disclosed by local attraction basins, and the periodic burster and multi-scroll chaotic burster are found if a multi-level pulse current is used to imitate a periodical external stimulus on the neurons. The Hamiltonian energy function is calculated and analyzed with or without external excitation. Finally, the neuronal circuit is designed and implemented, which can mimic electrical activity of the neurons and is useful for physical applications. The experimental results captured from the analog circuit are consistent well with the numerical simulation results.
Highlights
In 1971, by deducing from the perspective of logic, Chua pointed out that there should be a circuit element linking magnetic flux and electric charge, and enriches the relationships among the electric quantities [1]
Liang et al [11] proposed an S-type locally active memristor, constructed an equivalent analog circuit, and a small signal equivalent analog circuit that is used to reveal the influence on the amplification of extremely small fluctuation in energy in the locally active region
It is found that the variation of the memristive parameters causes the change of locally active region, and determines the existence of local activity, which is an interesting phenomenon, and may be helpful to construct different type locally active memristors, such as N-type [14] and M-type locally active memristors
Summary
In 1971, by deducing from the perspective of logic, Chua pointed out that there should be a circuit element linking magnetic flux and electric charge, and enriches the relationships among the electric quantities [1]. A bi-stable non-volatile locally active memristor with complex dynamics was proposed and analyzed in [12]. Some published papers have pointed out the non-volatile locally active memristors can be utilized to describe electromagnetic induction or as a memristive synapse. By introducing hyperbolic tangent function, Wang et al presented a bi-stable scissors-type locally active memristor which was utilized as an autapse in two Hindmarsh-Rose neural networks [24]. To investigate the characteristics of the new proposed bistable threshold locally active memristor based neuron network, this new memristor is introduced to the modified FitzHugh-Nagumo(FHN) nervous system, which was proposed by [30], as a coupled synapse.
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