MMN-2513

Stability and bifurcation analysis for a delayed Shimizu-Morioka model

Xin Zhang;

Abstract

This paper is concerned with a Shimizu-Morioka model with constant delays. Its stability of the equilibrium is investigated and the existence of Hopf bifurcations is demonstrated by analyzing the associated characteristic equation. Furthermore, the explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the center manifold theory and the normal form method. Finally, special attention is paid to numerical simulations in order to verify the theoretical predictions.


Vol. 20 (2019), No. 1, pp. 585-598
DOI: 10.18514/MMN.2019.2513


Download: MMN-2513