In this paper, a 3D jerk chaotic system with hidden attractor was explored, and the dissipativity, equilibrium, and stability of this system were investigated. The attractor types, Lyapunov exponents, and Poincare section of the system under different parameters were analyzed. Additionally, a circuit was carried out, and a good similarity between the circuit experimental results and the theoretical analysis testifies the feasibility and practicality of the original system. Furthermore, a robust feedback controller was designed based on the finite-time stability theory, which guarantees the synchronization of 3D jerk master-slave system in finite time and asymptotically converges to the origin. Finally, we also give verification for the discussion in this paper by numerical simulation.

No abstract

The synchronization of coupled neurons has been an important field of study in neuroscience. In this paper, the synchronization in coupled map-based neurons is studied. It is assumed that the neurons are coupled via a memristor. Firstly, the case of two-coupled neurons is investigated, and then two neurons are used as the units of a ring network. It is shown that the memristive coupling coefficient and the initial condition of the flux variable affect the synchronization of two neurons. By increasing the memristive coupling coefficient, multiple synchronous and asynchronous regions are observed. In the ring network, two neurons in each unit can become synchronous, but the whole network does not reach complete synchronization.

The ideal magnetic flux-controlled memristor was introduced into a four-dimensional chaotic system and combined with fractional calculus theory, and a novel four-dimensional commensurate fractional-order system was proposed and solved using the Adomian decomposition method. The system orders, parameters, and initial values were studied as independent variables in the bifurcation diagram and Lyapunov exponents spectrum, and it was discovered that changing these variables can cause the system to exhibit more complex and rich dynamical behaviors. The system had an offset boosting, which was discovered by adding a constant term after the decoupled linear term. Finally, the results of the numerical simulation were verified through the use of analog circuits and FPGA designs, and a control scheme for the system circuit was also suggested.

No abstract