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This study comprehensively investigates synchronization control of the memristive- and resistive-coupled neural network with noise effect. In this context, a sub-network is constructed with three chaotic memristive Hindmarsh–Rose neurons coupled by the memristive synapses. Then, two equivalent sub-networks are linked by the diffusive resistive synapse under a distinctive global network structure including two sub-networks. Thus, a double (memristive/resistive) control mechanism is used to achieve the synchronization state. The first mechanism is the memristive synaptic coupling in each sub-network, and the second one is the diffusive resistive coupling between two sub-networks constructing the global network. The synchronization between the neurons is proven theoretically through the Lyapunov stability and Lipschitz theorems and this proof process is verified with numerical experiments. According to the theoretical and numerical results, by adjusting memristive/resistive synaptic coupling weights, a synchrony behavior is generated successfully in these sub-networks and global networks. Additionally, this paper also handles the Gaussian white noise effect on the global network to examine continuity capability and stability of synchronization. Two different frameworks are built by applying the noise with multiple noise power levels and periods to (i) one of the resistive coupling neurons in each sub-network directly and (ii) one neuron in a sub-network without direct contact with the other sub-network. With these two characteristic designs, it is proven that the second design provides more robust characteristics since it utilizes the double control mechanism, which enhances the stability throughout external interferences enabling the network to sustain synchronous states. [ABSTRACT FROM AUTHOR]

While using polynomial functions to define window functions is an initial approach in studying the memristor element, it is susceptible to generating imaginary results. However, using window functions, including the trigonometric function, is a current field of research on the memristor element. This paper uses the trigonometric Blackman window function to present a new memristor element model and investigates its nonlinear ion drift model properties. The motivation of this study is the usage of the trigonometric Blackman window function, which presents a more detailed definition and leads to more accurate results in windowing operations. The Blackman window function can address the issues of border locking and terminal state. Numerical simulations have verified this proposed structure. Additionally, the analog realizations of the memristor element constructed with the Blackman window function have been achieved on a Field Programmable Analog Array, which offers fast prototyping, serving as an alternative approach for emulating memristors. [ABSTRACT FROM AUTHOR]