Nonlinear analysis and minimum L2-norm control in memcapacitor-based hyperchaotic system via online particle swarm optimization

•A physical memristive device is considered to analyze a new hyperchaotic system.•A fully autonomous hyperchaotic systems based on a physical memristor and memcapacitor is here considered.•An original physical model of HP memristor based on the movement of the boundary between the two regions by causing the charged dopants to drift, and charge-controlled memcapacitor is applied in the proposed hyperchaotic system.•A mathematical model of the circuit is derived, confirming the role of the memristor and memcapcitor nonlinearity in chaos generation.•A simple feedback control is considered to chaos control of memcapacitor based hyperchaotic memristor oscillator.•In order to Hchaos control of memcapacitor based hyperchaotic memristor oscillator, an online particle swarm optimization (PSO) technique is developed to design the feedback control using L2–norm minimization. Memristor and memcapacitor are two novel memristive devices. Memristive nonlinear elements behave like synapses in the nervous system. In this study, an original physical model of HP memristor is presented based on the movement of the boundary between the doped and undoped regions by causing the charged dopants to drift. Furthermore, a charge-controlled memcapacitor is used to design a novel hyperchaotic oscillator. It is found that the hyperchaotic oscillator, which is based on memristor and memcapacitor, can realize high-security data encryption. Then, the problem of controlling chaos is addressed in the proposed memcapacitor-based hyperchaotic memristor oscillator using a simple feedback control. Moreover, in this study, a novel approach is used to stabilize chaos using the L2–norm minimization method. The feedback control is applied to minimize the L2–norm of state variables as the cost function. An online particle swarm optimization (PSO) technique is developed to design the feedback control using L2–norm minimization. The sensitivity to initial condition is examined for different initial conditions. The proposed technique can be used for chaos stabilization in a complex dynamic system.