Delay-dependent parameters bifurcation in a fractional neural network via geometric methods

Delayed fractional neural network models are addressed to describe the effects of signal losses due to delay, the memory of neurons and self-feedback delay on the dynamics. The stable intervals of communication delay are first determined when the self-feedback delay is absent. The network with signal losses can exhibit stability switches. Then, the criteria for the generation of Hopf bifurcation for self-feedback delay are established by treating communication delay as a constant and it is shown that self-feedback delay can induce changes in stability for the equilibrium as it crosses the first Hopf bifurcation point. The stable regions in the delay plane are also plotted by the geometric method. Finally, two illustrative examples are provided to corroborate the efficiency of the procured results. The obtained results illustrate that the stable regions for delays become larger as fractional order decreases, which indicates that the memory of neurons can dampen the oscillatory behaviors.