Finite-time Synchronization Control of the Hyperchaotic Systems with Intersecting Terms

The global finite-time synchronization control of a type of fourth-order hyperchaotic systems with intersecting nonlinearities was studied. Firstly, the matrix form of this kind of hyperchaotic system was given to construct the master-slave synchronization models based on the generalized linear state error feedback controller. Then, the finite-time synchronization problem was equivalent to the finite-time stability of the error system originating from the master-slave hyperchaotic systems. The global finite-time stability of the error system was proven by the finite-time stability theory, further obtaining the criterion for global finite-time synchronization and the synchronization time estimation in mathematical formula. Subsequently, the theoretical results were applied to the well-known hyperchaotic Lorenz-stenflo system. The finite-time synchronization criteria for hyperchaotic Lorenz-stenflo systems were further proven by using optimization technology, and the corresponding synchronization times were estimated. Finally, the simulation was conducted by the MATLAB software, showing that two hyperchaotic Lorenz-stenflo systems could synchronize in a finite time.