In this paper, we focus on the Hopf bifurcation control of a small-world network model with time-delay.
With emphasis on the relationship between the Hopf bifurcation and the time-delay, we investigate the effect of
time-delay by choosing it as the bifurcation parameter. By using tools from control and bifurcation theory, it is
proved that there exists a critical value of time-delay for the stability of the model. When the time-delay passes
through the critical value, the model loses its stability and a Hopf bifurcation occurs. To enhance the stability of
the model, we propose an improved hybrid control strategy in which state feedback and parameter perturbation
are used. Through linear stability analysis, we show that by adjusting the control parameter properly, the onset
of Hopf bifurcation of the controlled model can be delayed or eliminated without changing the equilibrium point
of the model. Finally, numerical simulations are given to verify the theoretical analysis.
DING Daweia,b* (丁大为), ZHANG Xiaoyunb (张肖芸), WANG Niana,b* (王年), LIANG Donga,b (梁栋)
. Hybrid Control of Delay Induced Hopf Bifurcation of Dynamical Small-World Network[J]. Journal of Shanghai Jiaotong University(Science), 2017
, 22(2)
: 206
-215
.
DOI: 10.1007/s12204-017-1823-7
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