The memristor can change its resistance according to the amount of electric charge flowing through it, which is very similar to the update of synaptic weights of neurons under the external stimulation. Thus, using memristor as a coupled synapse will play an important role in building future neural networks. In this study, a tangent type memristor is used to couple two heterogeneous neurons and the memristor model is described as
$$\left\{\begin{array}{c}{I}_{1}=W\left({}_{1}\right){v}_{1}=\left(\alpha -\beta tanh\left({}_{1}\right)\right){v}_{1}\\ \frac{d{}_{1}}{dt}=-{}_{1}+{v}_{1} \end{array}\right.$$
1
where \({I}_{1}\),\({}_{1}\),\({v}_{1}\) represent the output current, memristor’s internal state and input voltage, respectively, W(\({}_{1}\)) = \(\left(\alpha -\beta tanh\left({}_{1}\right)\right)\) is memductance function, α and β are the memristive parameters.
When neurons are exposed to the external electromagnetic radiation, magnetic flux passes through their cell membranes. According to Faraday’s law of electromagnetic induction, the impact of electromagnetic radiation on each neuron is equivalent to the current induced by the external magnetic flux traversing the cell membrane. So, we use a flux-controlled memristor to simulate the effect of electromagnetic radiation on neurons, which can be expressed as
$$\left\{\begin{array}{c}{I}_{2}=W\left({}_{2}\right){v}_{2}={tanh\left({}_{2}\right)v}_{2} \\ \frac{d{}_{2}}{dt}={}_{2}\left(m-n\left|{}_{2}\right|\right)+{v}_{2} \end{array}\right.$$
2
where,\({I}_{2}\),\({}_{2}\),\({v}_{2}\) represent the electromagnetic radiation current, internal state and voltage respectively, W(\({}_{2}\)) = tanh(\({}_{2}\)) is memductance function, m and n are the memristive parameters.
In this paper, the tangent type memristor (1) is considered as the coupling synapse to bridge HR and FHN neurons. Inevitably, both neurons are subjected to the external electromagnetic radiation. Thus, the flux-controlled memristor (2) can be used to model the electromagnetic radiation effect. A memristive synapse coupled a heterogeneous neuron network exposed to external electromagnetic radiation is depicted in Fig. 1, the model can be written as Fig. 1 Memristor-coupled heterogeneous neuron network exposed to the external electromagnetic radiation, where the memristor M1 is considered as the coupled synapse, M2 and M3 simulate the effect of electromagnetic radiation.
$$\left\{\begin{array}{c}\frac{d{x}_{1}}{dt}={y}_{1}-{a}_{1}{x}_{1}^{3}+{b}_{1}{x}_{1}^{2}+{k}_{1}\left(-\beta tanh\left({}_{1}\right)\right)\left({x}_{1}-{x}_{2}\right)+{k}_{2}tanh\left({}_{2}\right){x}_{1} \\ \frac{d{y}_{1}}{dt}={c}_{1}-{d}_{1}{x}_{1}^{2}-{y}_{1} \\ \frac{d{x}_{2}}{dt}=\frac{1}{{a}_{2}}\left({x}_{2}-\frac{1}{3}{x}_{2}^{3}-{y}_{2}\right)-{k}_{1}\left(-\beta tanh\left({}_{1}\right)\right)\left({x}_{1}-{x}_{2}\right)+{k}_{3}tanh\left({}_{3}\right){x}_{2} \\ \frac{d{y}_{2}}{dt}=\left({x}_{2}-{b}_{2}{y}_{2}+{c}_{2}\right) \\ \frac{d{}_{1}}{dt}={-}_{1}+\left({x}_{1}-{x}_{2}\right) \\ \frac{d{}_{2}}{dt}={}_{2}\left(m-n\left|{}_{2}\right|\right)+{x}_{1} \\ \frac{d{}_{3}}{dt}={}_{3}\left(m-n\left|{}_{3}\right|\right)+{x}_{2} \\ \end{array}\right.$$
3
where\({x}_{1},{y}_{1} and {x}_{2}, {y}_{2}\)represent the membrane voltages of HR and FHN neurons, respectively, k1 is the coupling strength, k2 and k3 are electromagnetic radiation intensities. The other system parameters are determined as a1 = 1, b1 = 3, c1 = 1, d1 = 5, a2 = 0.2, b2 = 0.2, c2 = 0.6, α = 7, β = 0.5, m = 5, n = 1.