Performance specifications place restrictions on the dynamic response of many systems, including power systems. It is often convenient to know parameter values that induce limiting behaviour, i.e., force the system to just meet the specification. This limiting behaviour is a form of grazing bifurcation, and can be formulated as a boundary value problem. The paper develops a numerical shooting m...

In this paper, a duopoly game model with double delays in hydropower market is established, and the research focus on the influence of time delay parameter on the complexity of the system. Firstly, we established a game model for the enterprises considering both the current and the historical output when making decisions. Secondly, the existence and stability of Hopf bifurcation are analyzed, a...

In this study, we propose a novel discrete-time coupled model to generate oscillatory responses via periodic points with a high periodic order. Our coupled system comprises one-dimensional oscillators based on the Rulkov map and a single globally coupled oscillator. Because the waveform of a one-dimensional oscillator has sharply defined peaks, the coupled system can be applied to dynamic image...

We present a mathematical model of a neural mass developed by a number of people, including Lopes da Silva and Jansen. This model features three interacting populations of cortical neurons and is described by a six-dimensional nonlinear dynamical system. We address some aspects of its behavior through a bifurcation analysis with respect to the input parameter of the system. This leads to a comp...

Bifurcation control deals with modification of bifurcation characteristics of a parameterized nonlinear system by a designed control input. Typical bifurcation control objectives include delaying the onset of an inherent bifurcation, stabilizing a bifurcated solution or branch, changing the parameter value of an existing bifurcation point, modifying the shape or type of a bifurcation chain, int...

Grazing bifurcations in impact oscillators characterize the transition in asymptotic dynamics between impacting and non-impacting motions. Several different grazing bifurcation scenarios under variations of a single system parameter have been previously documented in the literature. In the present paper, the transition between two characteristically different co-dimension-one grazing bifurcatio...

This paper characterizes the attractor structure of synchronous and asynchronous Boolean networks induced by bithreshold functions. Bi-threshold functions are generalizations of standard threshold functions and have separate threshold values for the transitions 0 → 1 (up-threshold) and 1 → 0 (down-threshold). We show that synchronous bi-threshold systems may, just like standard threshold system...

the modeling investigation in this paper discusses the system level effects of a toxicant on a three species food chain system. in the models, we have assumed that the presence of top predator reduces the predatory ability of the intermediate predator. the stability analysis of the models is carried out and the sufficient conditions for the existence and extinction of the populations under the ...

Various bifurcations exist in nonlinear dynamical systems such as complex circuits, networks, and devices. Bifurcations can be important and beneficial if they are under appropriate control. Bifurcation control and anti-control deal with modification of system bifurcative characteristics by a designed control input. Typical bifurcation control and anti-control objectives include delaying the on...