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The purpose of this paper is to develop new four-dimensional (4D) hyperchaotic system by adding another state variable and linear controller to three-dimensional T chaotic dynamical systems. Its dynamical analyses, circuit experiment, control and synchronization applications are presented.

A new 4D hyperchaotic attractor is achieved through a simulation, circuit experiment and mathematical analysis by obtaining the Lyapunov exponent spectrum, equilibrium, bifurcation, Poincaré maps and power spectrum. Moreover, hardware experimental measurements are performed and obtained results well validate the numerical simulations. Also, the passive control method is presented to make the new 4D hyperchaotic system stable at the zero equilibrium and synchronize the two identical new 4D hyperchaotic system with different initial conditions.

The passive controllers can stabilize the new 4D chaotic system around equilibrium point and provide the synchronization of new 4D chaotic systems with different initial conditions. The findings from Matlab simulations, circuit design simulations in computer and physical circuit experiment are consistent with each other in terms of comparison.

The 4D hyperchaotic system is presented, and dynamical analysis and numerical simulation of the new hyperchaotic system were firstly carried out. The circuit of new 4D hyperchaotic system is realized, and control and synchronization applications are performed.