In this paper, stability and bifurcation of piecewise affine systems is investigated. In the stability analysis, stability of the origin and existence of limit cycles are investigated by means of the radial growth rate, which describes the behavior of the radial direction of the trajectories. In the bifurcation analysis, Hopf bifurcation and saddle-node bifurcation is discussed. The radial grow...

In this paper, the bifurcation analysis for Burgers mapping has been studied. The existence and stability of the fixed points of this map was derived. The conditions of existence for pitchfork bifurcation, flip bifurcation and Neimark-Sacker bifurcation are derived by using center manifold theorem and bifurcation theory. The control of the map around stable NeimarkSacker bifurcation has been ac...

Lorenz like attractors are known to appear in unfoldings from certain codimension two homoclinic bifurcations for differential equations in R that possess a reflectional symmetry. This includes homoclinic loops under a resonance condition and the inclination flip homoclinic loops. We show that Lorenz like attractors also appear in the third possible codimension two homoclinic bifurcation (for h...

Abstract. This paper is concerned with the deterministic and the stochastic delayed Kaldor–Kalecki nonlinear business cycle models of the income. They will take into consideration the investment demand in the form suggested by Rodano. The existence of the Hopf bifurcation is studied and the direction and the local stability of the Hopf bifurcation is also taken into consideration. For the stoch...

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 ...

The effect of additive white noise on a model for bursting behavior in large aspectratio binary fluid convection is considered. Such bursts are present in systems with nearly square symmetry and are the result of heteroclinic cycles involving infinite amplitude states created when the square symmetry is broken. A combination of numerical results and analytical arguments show how even a very sma...

In this paper, a stage-structured epidemic model with a nonlinear incidence is investigated. By carrying out global qualitative and bifurcation analysis, it is shown that the model exhibits the bistability and undergoes the Hopf bifurcation and the Bogdanov-Takens bifurcation. Moreover, several numerical simulations are given to support the theoretical analysis.

Consider nonlinear dynamical systems modelled by parameterised differential and difference equations. When the values of the system parameters vary from those at which the system is currently operated, it can exhibit qualitative changes in behaviour and a steady-state may disappear or become unstable through a bifurcation [1, 2]. Bifurcation analysis is clearly useful and a bifurcation diagram ...

Abstract Analytical determination of the bifurcation thresholds is of important interest for practical electrical machine design and analysis control. This paper presents mathematical investigation of the qualitative behavior of indirect filed oriented control induction motor based on bifurcation theory. In this context, steady-state responses analysis of the motor model is discussed and an ana...

In this paper, we consider the impact of time delay by media on the control of the disease. We set up a class of SISM epidemic model with the time delay and the cumulative density of awareness caused by media. The sufficient condition of global asymptotic stability of disease-free equilibrium is approved. We get the global stability of the epidemic equilibrium and the existence conditions of Ho...