Bifurcation analysis on a two-neuron system with distributed delays

By X. Liao, Kwok-wo Wong, Zhongfu Wu. 2001

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Approximating the Stability Region for a Differential Equation with a Distributed Delay (2009, unknown): “[23, 29]) specific kernels (usually the gam ma distribution withp = 1 or p = 2) are put into the model and the resulting behaviour is analyzed in etail.”
(Corr. to) Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach (2002, methodology): “Considering the delay-dependent stability for systems with time-varying delays, several attempts have been reported (Joy, 1999b, 2000a; Liao et al., 2001a,b,c).”
Order reduction of retarded nonlinear systems – the method of multiple scales versus center-manifold reduction (2008, methodology): “where g( ˆ x) is a general three-times continuously differentiable function, τ> 0, and β> 0. Liao et al. [ 18 ] constructed the normal form of the Hopf bifurcations of this equation using a combination of the centermanifold theorem and the method of normal forms [19].”
Global existence of periodic solutions in a tri-neuron network model with delays (2004, background): “AMS Subject Classifications: 34K13, 34K18,92B20 Keywords: Neural networks; Time delay; Global Hopf bifurcation; Periodic solutions”