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Stability analysis has been always a key issue in nonlinear dynamics and engineering applications, and it is still a challenging task for time-delay control systems when tuning some parameters like feedback gains and delays. In this paper, firstly we propose a parametric continuation algorithm for calculating the rightmost characteristic root(s), by solving initial value problems of a nonlinear differential equation associated with the characteristic function of the time-delay system. Then we study the static bifurcation caused by multiple characteristic roots that occurs in solving the associated nonlinear initial value problems and present an algorithm for fast calculation of the bifurcation points. We demonstrate the theoretical results with examples arising in vibration control. [ABSTRACT FROM AUTHOR]

This paper studies the nonlinear dynamics of coupled ring networks each with an arbitrary number of neurons. Different types of time delays are introduced into the internal connections and couplings. Local and global asymptotical stability of the coupled system is discussed, and sufficient conditions for the existence of different bifurcated oscillations are given. Numerical simulations are performed to validate the theoretical results, and interesting neuronal activities are observed, such as rest state, synchronous oscillations, asynchronous oscillations, and multiple switches of the rest states and different oscillations. It is shown that the number of neurons in the sub-networks plays an important role in the network characteristics. [ABSTRACT FROM AUTHOR]