Elimination of oscillation causing Hopf bifurcations in engineering problems

Bifurcation analysis was performed on various engineering process problems that exhibit undesirable oscillation causing Hopf bifurcations. Hopf bifurcations result in oscillatory behavior which is problematic for optimization and control tasks. Additionally, the presence of oscillations causes a reduction in product quality and in some cases causes equipment damage. The hyperbolic tangent function activation factor is normally used in neural networks and optimal control problems to eliminate spikes in optimum profiles. Spikes are similar to oscillatory profiles and this is the motivation to investigate whether the hyperbolic tangent function activation factor can eliminate the oscillation causing Hopf bifurcations. The results of this paper show that the hyperbolic tangent function activation factor eliminates the Hopf bifurcations. Bifurcation analysis is performed using The MATLAB software MATCONT. Five examples involving problems that exhibit Hopf bifurcations are presented.