Junwei Wang

Mixed outer synchronization of coupled complex networks with time-varying coupling delay

In this paper, the problem of outer synchronization between two complex networks with the same topological structure and time-varying coupling delay is investigated. In particular, we introduce a new type of outer synchronization behavior, i.e., mixed outer synchronization (MOS), in which different state variables of the corresponding nodes can evolve into complete synchronization, antisynchronization, and even amplitude death simultaneously for an appropriate choice of the scaling matrix. A novel nonfragile linear state feedback controller is designed to realize the MOS between two networks and proved analytically by using Lyapunov-Krasovskii stability theory. Finally, numerical simulations are provided to demonstrate the feasibility and efficacy of our proposed control approach.

Chaos Control of a Fractional-Order Financial System

Fractional-order financial system introduced by W.-C. Chen (2008) displays chaotic motions at order less than 3. In this paper we have extended the nonlinear feedback control in ODE systems to fractional-order systems, in order to eliminate the chaotic behavior. The results are proved analytically by applying the Lyapunov linearization method and stability condition for fractional system. Moreover numerical simulations are shown to verify the effectiveness of the proposed control scheme.

Partial synchronization in coupled chemical chaotic oscillators

In this paper we investigate the problem of partial synchronization in diffusively coupled chemical chaotic oscillators with zero-flux boundary conditions. The dynamical properties of the chemical system which oscillates with Uniform Phase evolution, yet has Chaotic Amplitudes (UPCA) are first discussed. By combining numerical and analytical methods, the impossibility of full global synchronization in a network of two or three coupled chemical oscillators is discovered. Mathematically, stable partial synchronization corresponds to convergence to a linear invariant manifold of the global state space. The sufficient conditions for exponential stability of the invariant manifold in a network of three coupled chemical oscillators are obtained via the nonlinear contraction principle.

Synchronization of fractional-order linear complex networks

In this paper, we concentrate on the synchronization problem of fractional-order complex networks with general linear dynamics under connected topology. By introducing a pseudo-state transformation, the problem is converted into an equivalent simultaneous stabilization problem of independent subsystems, which is characterized by nonzero eigenvalues of the Laplacian matrix. Then, sufficient conditions in terms of linear matrix inequalities (LMIs) for synchronization are established, which can be easily solved by efficient convex optimization algorithms. Finally, three examples are provided to illustrate the effectiveness of the proposed method.

Adaptive Leader-Following Consensus of Multi-Agent Systems with Unknown Nonlinear Dynamics

This paper deals with the leader-following consensus of multi-agent systems with matched nonlinear dynamics. Compared with previous works, the major difficulty here is caused by the simultaneous existence of nonidentical agent dynamics and unknown system parameters, which are more practical in real-world applications. To tackle this difficulty, a distributed adaptive control law for each follower is proposed based on algebraic graph theory and algebraic Riccati equation. By a Lyapunov function method, we show that the designed control law guarantees that each follower asymptotically converges to the leader under connected communication graphs. A simulation example demonstrates the effectiveness of the proposed scheme.

Pinning synchronization of fractional-order complex networks with Lipschitz-type nonlinear dynamics

This paper deals with pinning synchronization problem of fractional-order complex networks with Lipschitz-type nonlinear nodes and directed communication topology. We first reformulate the problem as a global asymptotic stability problem by describing network evolution in terms of error dynamics. Then, a novel frequency domain approach is developed by using Laplace transform, algebraic graph theory and generalized Gronwall inequality. We show that pinning synchronization can be ensured if the extended network topology contains a spanning tree and the coupling strength is large enough. Furthermore, we provide an easily testable criterion for global pinning synchronization depending on fractional-order, network topology, oscillator dynamics and state feedback. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Adaptive consensus of nonlinear multi-agent systems with unknown backlash-like hysteresis

In this brief, we consider the consensus problem of high-order nonlinear multi-agent systems with unknown backlash-like hysteresis and unknown control direction. By using backstepping technique, a distributed adaptive control scheme, with the adoption of Nussbaum-type function, is developed to solve this consensus problem. Radial basis function neural network is employed to neutralize the uncertain nonlinear dynamics. The approximation error of the neural networks, together with external disturbance and a bounded term from the hysteresis model, is adaptively estimated and counteracted by a robust term. Under undirected connected communication topology, it is proved that the consensus can be achieved asymptotically with the proposed control protocol. Finally, a numerical example is presented to illustrate the performance of the proposed protocol. HighlightsUnknown backlash-like hysteresis and unknown control direction are considered.Dynamics of the systems are high-order with unknown nonlinear dynamics.A modified robust strategy is employed to deal with approximation error.

cAMP-regulated dynamics of the mammalian circadian clock.

Previous molecular description of the mammalian timekeeping mechanism was based mainly on transcriptional/translational feedback loops (TTFLs). However, a recent experimental report challenges such a molecular architecture, showing that the cAMP signaling is an indispensable component of the mammalian circadian clock. In this paper, we develop a reduced mathematical model that characterizes the mammalian circadian network. The model with 8-state differential equations incorporates both TTFLs and cAMP-mediated feedback loop. In agreement with experimental observations, our results show that: (1) the model simulates sustained circadian (23.4-h periodic) oscillations in constant darkness and entrained circadian dynamics by light-dark cycles; (2) circadian rhythmicity is lost without cAMP signaling; (3) the system is resilient to large fluctuations in transcriptional rates; (4) it successfully simulates the phenotypes of Per1(-/-)/Per2(-/-) double-mutant mice and Bmal1(-/-) mutant mice. Our study implies that to understand the circadian pacemaking in suprachiasmatic nucleus neurons, the TTFLs should not be isolated from intracellular cAMP-dependent signaling.

Consensus of multi-agent nonlinear dynamic systems under slow switching topology

This paper is devoted to the consensus problem of multi-agent systems with inherent nonlinear dynamics. To reflect the practical environment of multi-agent systems, the communication topology is assumed to switch slowly within a finite set of directed topologies restricted by an average dwell time switching signal. By taking advantage of tools from switched systems and piecewise Lyapunov functions, it is shown that consensus can be guaranteed for the choice of suitable parameters if each topology contains a directed spanning tree. Explicit analytical conditions on both feedback gain and average dwell time of admissible switching signals for consensus are also offered. Finally, an example with computer simulation is provided to illustrate the theoretical results.

Positive Feedback-Assisted Short/Long-Range Cell Signalings In Mapk Cascades

In this paper, we study potentials of positive feedback in spatial phosphoprotein signal propagation. For this, we consider a signaling pathway of four-tiered protein kinase cascades with each tier involving single (de)phosphorylation reactions only. In the case of a small cell, we propose a short positive feedback for short-range cell signaling, which can generate bistability to facilitate the phosphoprotein signal propagation from the plasma membrane to the periphery of cell nucleus. In contrast, in the case of a large cell for which the long-range signaling cannot be achieved by the short feedback, we propose a long positive feedback, and find that it can facilitate the propagation of phosphoprotein signal over a long distance. These results imply that positive-feedback mechanisms would be employed by living organisms for spatial information transfer and cellular decision-making processing.