Topological geometry analysis for complex dynamic systems based on adaptive control method

Abstract

Several models had been proposed for dynamic systems, and different criteria had been analyzed for such models such as Hamiltonian, synchronization, Lyapunov expansion, and stability. The geometry criteria play a significant part in analyzing dynamic systems and some study articles analyze the geometry of such topics. The synchronization and the complex-network control with specified topology; meanwhile, the exact topology may be unknown. In the present paper, and by making use of the adaptive control method, a proposed control method is developed to determine the actual topology. The basic idea in the proposed method is to receive evolution of the network-nodes