This paper offeres an exact study on the robust stability of a kind of combined integrating control system, and the robust stability belongs to the analysis of a kind of quasi-polynomial with two independent time dela...This paper offeres an exact study on the robust stability of a kind of combined integrating control system, and the robust stability belongs to the analysis of a kind of quasi-polynomial with two independent time delays. The parameters of stable space under time delay uncertainty are fixed after Rekasius transformation, and then a new cluster treatment of characteristic roots (CTCR) procedure is adopted to determine the stable space. By this strategy we find that the unstable space is not continuous and both Karitonov vertices theory and Edge theory are unable to be extended to quasi-polynomial under time delay uncertainty.展开更多
In this paper, we study delay-induced firing behavior and transitions in adaptive Newman-Watts networks of thermosensitive neurons with electrical or chemical synapses. It is found that electrical and chemical synapse...In this paper, we study delay-induced firing behavior and transitions in adaptive Newman-Watts networks of thermosensitive neurons with electrical or chemical synapses. It is found that electrical and chemical synapse time delay-induced firing behavior and transitions differ significantly. In the case of electrical synapses, the bursts for a fixed delay involve equal number of spikes in each burst, and for certain time delays the firing can be inhibited. However, in the case of chemical synapses the bursts for a fixed delay involve different numbers of spikes in each burst, and no firing inhibition is observed. It is also shown that larger growth rates of adaptive coupling strength or larger network randomness can enhance the synchronization of bursting in the case of electrical synapses but reduce it in the case of chemical synapses. These results show that electrical and chemical synapses have different effects on delay-induced firing behavior and dynamical evolution. Compared to electrical synapses, chemical synapses might be more beneficial to the generation of firing and abundant firing transitions in adaptive and delayed neuronal networks. These findings can help to better understand different firing behaviors in neuronal networks with electrical and chemical synapses.展开更多
In this paper, inertia is added to a simplified neuron system with time delay. The stability of the trivial equilibrium of the net- work is analyzed and the condition for the existence of Hopf bifurcation is obtained ...In this paper, inertia is added to a simplified neuron system with time delay. The stability of the trivial equilibrium of the net- work is analyzed and the condition for the existence of Hopf bifurcation is obtained by discussing the associated characteristic equation. Hopf bifurcation is investigated by using the perturbation scheme without the norm form theory and the center man- ifold theorem. Numerical simulations are performed to validate the theoretical results and chaotic behaviors are observed. Phase plots, time history plots, power spectra, and Poincar6 section are presented to confirm the chaoticity. To the best of our knowledge, the chaotic behavior in this paper is new to the previously published works.展开更多
基金National Natural Science Foundation of China (No.60674088)
文摘This paper offeres an exact study on the robust stability of a kind of combined integrating control system, and the robust stability belongs to the analysis of a kind of quasi-polynomial with two independent time delays. The parameters of stable space under time delay uncertainty are fixed after Rekasius transformation, and then a new cluster treatment of characteristic roots (CTCR) procedure is adopted to determine the stable space. By this strategy we find that the unstable space is not continuous and both Karitonov vertices theory and Edge theory are unable to be extended to quasi-polynomial under time delay uncertainty.
文摘In this paper, we study delay-induced firing behavior and transitions in adaptive Newman-Watts networks of thermosensitive neurons with electrical or chemical synapses. It is found that electrical and chemical synapse time delay-induced firing behavior and transitions differ significantly. In the case of electrical synapses, the bursts for a fixed delay involve equal number of spikes in each burst, and for certain time delays the firing can be inhibited. However, in the case of chemical synapses the bursts for a fixed delay involve different numbers of spikes in each burst, and no firing inhibition is observed. It is also shown that larger growth rates of adaptive coupling strength or larger network randomness can enhance the synchronization of bursting in the case of electrical synapses but reduce it in the case of chemical synapses. These results show that electrical and chemical synapses have different effects on delay-induced firing behavior and dynamical evolution. Compared to electrical synapses, chemical synapses might be more beneficial to the generation of firing and abundant firing transitions in adaptive and delayed neuronal networks. These findings can help to better understand different firing behaviors in neuronal networks with electrical and chemical synapses.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11202068 and 11032009)
文摘In this paper, inertia is added to a simplified neuron system with time delay. The stability of the trivial equilibrium of the net- work is analyzed and the condition for the existence of Hopf bifurcation is obtained by discussing the associated characteristic equation. Hopf bifurcation is investigated by using the perturbation scheme without the norm form theory and the center man- ifold theorem. Numerical simulations are performed to validate the theoretical results and chaotic behaviors are observed. Phase plots, time history plots, power spectra, and Poincar6 section are presented to confirm the chaoticity. To the best of our knowledge, the chaotic behavior in this paper is new to the previously published works.
