Publications

This paper investigates the reconstruction problem for the Lorenz and Chen systems using noisy observation data. Both theoretical and numerical results show that the relatively accurate reconstruction of these two chaotic systems can be obtained under the condition of small random disturbance to the observations. These results also show that the model reconstruction accuracy can be enhanced by increasing the complexity of the underlying dynamical system.

We study synchronization transitions and pattern formation on small-world networks consisting of Morris–Lecar excitable neurons in dependence on the information transmission delay and the rewiring probability. In addition, networks formed via gap junctional connections and coupling via chemical synapses are considered separately. For gap-junctionally coupled networks we show that short delays can induce zigzag fronts of excitations, whereas long delays can further detriment synchronization due to a dynamic clustering anti-phase synchronization transition. For the synaptically coupled networks, on the other hand, we find that the clustering anti-phase synchronization can appear as a direct consequence of the prolongation of information transmission delay, without being accompanied by zigzag excitatory fronts. Irrespective of the coupling type, however, we show that an appropriate small-world topology can always restore synchronized activity if only the information transmission delays are short or moderate at most. Long information transmission delays always evoke anti-phase synchronization and clustering, in which case the fine-tuning of the network topology fails to restore the synchronization of neuronal activity.

The impact of inhibitory and excitatory synapses in delay-coupled Hodgkin–Huxley neurons that are driven by noise is studied. If both synaptic types are used for coupling, appropriately tuned delays in the inhibition feedback induce multiple firing coherence resonances at sufficiently strong coupling strengths, thus giving rise to tongues of coherency in the corresponding delay-strength parameter plane. If only inhibitory synapses are used, however, appropriately tuned delays also give rise to multiresonant responses, yet the successive delays warranting an optimal coherence of excitations obey different relations with regards to the inherent time scales of neuronal dynamics. This leads to denser coherence resonance patterns in the delay-strength parameter plane. The robustness of these findings to the introduction of delay in the excitatory feedback, to noise, and to the number of coupled neurons is examined. Mechanisms underlying our observations are revealed, and it is suggested that the regularity of spiking across neuronal networks can be optimized in an unexpectedly rich variety of ways, depending on the type of coupling and the duration of delays.

Buzzword-based viral marketing, known also as digital word-of-mouth marketing, is a marketing mode attached to some carriers on the Internet, which can rapidly copy marketing information at a low cost. Viral marketing actually uses a pre-existing social network where, however, the scale of the pre-existing network is believed to be so large and so random, so that its theoretical analysis is intractable and unmanageable. There are very few reports in the literature on how to design a spreading scheme for viral marketing on real social networks according to the traditional marketing theory or the relatively new network marketing theory. Complex network theory provides a new model for the study of large-scale complex systems, using the latest developments of graph theory and computing techniques. From this perspective, the present paper extends the complex network theory and modeling into the research of general viral marketing and develops a specific spreading scheme for viral marking and an approach to design the scheme based on a real complex network on the QQ instant messaging system. This approach is shown to be rather universal and can be further extended to the design of various spreading schemes for viral marketing based on different instant messaging systems.

Synchronization transitions are investigated in small-world neuronal networks that are locally modeled by the Rulkov map with additive spatiotemporal noise. In particular, we investigate the impact of different information transmission delays and rewiring probability. We show that short delays induce zigzag fronts of excitations, whereas intermediate delays can further detriment synchrony in the network due to a dynamic clustering anti-phase synchronization transition. Detailed investigations reveal, however, that for longer delay lengths the synchrony of excitations in the network can again be enhanced due to the emergence of in-phase synchronization. In addition, we show that an appropriate small-world topology can restore synchronized behavior provided information transmission delays are either short or long. On the other hand, within the intermediate delay region, which is characterized by anti-phase synchronization and clustering, differences in the network topology do not notably affect the synchrony of neuronal activity.

A time-delayed chaos control method based on repetitive learning is proposed. The integration of the repetitive learning control principle and the time delayed chaos control technique enables adaptive learning of appropriate control actions from learning cycles. In contrast to conventional repetitive learning control, no exact knowledge (analytic representation) of the target periodic orbits is needed, except for the time delay constant, which can be identified via either experiments or adaptive learning methods. To facilitate the discussion, the typical chaotic Duffing system is used as an example for illustration of the general methodology. Simulation result is provided to show the effectiveness of the proposed approach.