Narrow Results

In addition to border collision bifurcation, the time delay controlled two-cell DC/DC buck converter is shown to exhibit a chaotic behavior as well. The time delay controller adds new design parameters to the system and therefore the variation of a parameter may lead to different types of bifurcation. In this work, we present a thorough analysis of different scenarios leading to bifurcation and chaos. We show that the time delay controlled two-cell DC/DC buck converter may also exhibit a Neimark–Sacker bifurcation which for some parameter set may lead to a 2D torus that may then break yielding a chaotic behavior. Besides, the saturation of the controller can also lead to the coexistence of a stable focus and a chaotic attractor. The results are presented using numerical simulation of a discrete map of the two-cell DC/DC buck converter obtained by expressing successive crossings of Poincaré section in terms of each other.

In this paper, bifurcation analysis of a three-dimensional discrete game model is provided. Possible codimension-one (codim-1) and codimension-two (codim-2) bifurcations of this model and its iterations are investigated under variation of one and two parameters, respectively. For each bifurcation, normal form coefficients are calculated through reduction of the system to the associated center manifold. The bifurcations detected in this paper include transcritical, fold, flip (period-doubling), Neimark–Sacker, period-doubling Neimark–Sacker, resonance 1:2, resonance 1:3, resonance 1:4 and fold-flip bifurcations. Moreover, we depict bifurcation diagrams corresponding to each bifurcation with the aid of numerical continuation method. These bifurcation curves not only confirm our analytical results, but also reveal a richer dynamics of the model especially in the higher iterations.

The paper describes the Hick Samuelson Keynes dynamical economic model with discrete time and consumer sentiment. We seek to demonstrate that consumer sentiment may create fluctuations in the economical activities. The model possesses a flip bifurcation and a Neimark-Sacker bifurcation, after which the stable state is replaced by a (quasi-) periodic motion.