Generalized outer synchronization between non-dissipatively coupled complex networks with different-dimensional nodes. (English) Zbl 1480.34073
Summary: This paper investigates the generalized outer synchronization (GOS) between two non-dissipatively coupled complex dynamical networks (CDNs) with different time-varying coupling delays. Our drive-response networks also possess nonlinear inner coupling functions and time-varying outer coupling configuration matrices. Besides, in our network models, the nodes in the same network are nonidentical and the nodes in different networks have different state dimensions. Asymptotic generalized outer synchronization (AGOS) and exponential generalized outer synchronization (EGOS) are defined for our CDNs. Our main objective in this paper is to design AGOS and EGOS controllers for our drive-response networks via the open-plus-closed-loop control technique. Distinguished from most existing literatures, it is the partial intrinsic dynamics of each node in response network that is restricted by the QUAD condition, which is easy to be satisfied. Representative simulation examples are given to verify the effectiveness and feasibility of our GOS theoretical results in this paper.
MSC:
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K35 | Control problems for functional-differential equations |
| 90B10 | Deterministic network models in operations research |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
Keywords:
complex dynamical networks; asymptotic generalized outer synchronization; exponential generalized outer synchronization; non-dissipatively coupled; time-varying; different dimensionsReferences:
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