Due to their synaptic-like characteristics and memory properties, memristors are often used in neuromorphic circuits, particularly neural network circuits. However, most of the existing neural network circuits that can generate complex dynamics have high dimensions and excessive connections, which is not conducive to implementation. This article introduces a memristor containing an arctangent function into a simple cyclic neural network (SCNN) circuit to design a simple cyclic memristive neural network (SCMNN) circuit capable of generating complex multiscroll chaotic attractors. The designed SCMNN contains an external stimulus current and generates multiscroll attractors, with the number of scrolls expanding as the switches in the memristor equivalent circuit are activated. By varying the parameters, the multiscroll attractors can be broken into different numbers of coexisting attractors, which also depends on the switch, and it can achieve multivariable amplitude control when there is only one scroll. The anti-interference ability of the circuit is tested. A low-cost circuit-based microcontroller suitable for engineering applications is designed for it, and multiscroll attractors are successfully captured in an oscilloscope. The National Institute of Standards and Technology (NIST) test is carried out to verify its application value.