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 purpose of this paper is to study bifurcation of an Internet congestion control algorithm, namely REM (Random Exponential Marking) algorithm, with communication delay. By choosing the delay constant as a bifurcation parameter, we prove that REM algorithm exhibits Hopf bifurcation. The formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic so...

A bifurcation theory is applied to the multimachine power system to investigate the effect of iron saturation on the complex dynamics of the system. The second system of the IEEE second benchmark model of Subsynchronous Resonance (SSR) is considered. The system studied can be mathematically modeled as a set of first order nonlinear ordinary differential equations with (!=Xc/XL) as a bifurcation...

One of the important medical problems is infectious diseases such as HIV and hepatitis which annually causes the death of many people. So it is important to study infectious diseases parametric models. In this paper, we investigate differential equations system of HIV and hepatitis (with delay and without delay) from the stability and codimension-one bifurcation point of view. We show that thei...

A non-standard bifurcation, similar to a transcritical one, in a model of a bioreactor has been detected. This happens in a periodically-forced system with restrictions on the state space. The bioreactor is periodically fed with substrate. In the mathematical model, a periodic orbit approaches (without hitting) the restriction surface as a bifurcation parameter is varied. The way the orbit appr...

The stability of the predator-prey model subject to Allee effect is an interesting topic in recent times. impact a weak on discrete-time investigated this paper. Equilibrium analysis, and bifurcation theory are used examine mathematical properties proposed model. By using parameter as parameter, we provide sufficient conditions for flip bifurcation. Numerical simulations demonstrate our analyti...

Keywords: Bifurcation problems Hopf bifurcation Computational methods for bifurcation problems Attractors and their bifurcations a b s t r a c t An investigation into how well real bifurcations in the family of dynamical systems are approximated as the step-size varies is carried out. The preservation of bifurcation structures and stability under numerical simulations is discussed. In addition,...

In this paper, we consider a two-dimensional delay differential system with two delays. By analyzing the distribution of eigenvalues, linear stability of the equilibria and existence of Hopf, Bautin, and Hopf–Hopf bifurcations are obtained in which the time delays are used as the bifurcation parameter. General formula for the direction, period, and stability of the bifurcated periodic solutions...

Using the predictor-corrector scheme, the fractional-order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional-order diffusionless system for variation of the single control parameter is determined. The route to chaos is by period-doubling bifurcation in this fractional-order system, and some typical bifurcations are observed, such as the flip ...

The nonlinear dynamics such as bifurcation and chaos has got lot of attention in research fraternity. The power electronics is a dynamic and nonlinear field in which chaos plays an important role. The time dynamic and nonlinearity is cannot be neglected or it is default case in power electronics. The present paper discusses the simulative study of Bifurcation and chaotic behaviour in the single...