We consider C Hénon-like families of diffeomorphisms of R and study the boundary of the region of parameter values for which the nonwandering set is uniformly hyperbolic. Assuming sufficient dissipativity, we show that the loss of hyperbolicity is caused by a first homoclinic or heteroclinic tangency and that uniform hyperbolicity estimates hold uniformly in the parameter up to this bifurcation...

IIn this paper, using frequency domain approach, a single mode laser model with delay is investigated. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur when τ passes a sequence of critical values. This means that a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulat...

Three-species food-chain models, in which the prey population exhibits group defense, are considered. Using the carrying capacity of the environment as the bifurcation parameter, it is shown that the model without delay undergoes a sequence of Hopf bifurcations. In the model with delay it is shown that using a delay as a bifurcation parameter, a Hopf bifurcation can also occur in this case. The...

Abstract. In this paper, dynamical complexities of a three species food chain model with Holling type IV predator response is investigated analytically as well as numerically. The local and global stability analysis is carried out. The persistence criterion of the food chain model is obtained. Numerical bifurcation analysis reveals the chaotic behavior in a narrow region of the bifurcation para...

A new bifurcation critical criterion of flip-Neimark-Sacker bifurcation is proposed for detecting or anticontrolling this type of codimension-two bifurcation of discrete systems in a general sense. The criterion is built on the properties of coefficients of characteristic equations instead of the properties of eigenvalues of Jacobian matrix of nonlinear system, which is formulated using a set o...

We extend an investigation into the bifurcation phenomena exhibited by an oxidation reaction in an adiabatic reactor to the case of a diabatic reactor. The primary bifurcation parameter is the fuel fraction; the inflow pressure and inflow temperature are the secondary bifurcation parameters. The inclusion of heat loss in the model does not change the static steady-state bifurcation diagram; the...

In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given. Keyw...

In this paper, a nonlinear delay population model is investigated. Choosing the delay as a bifurcation parameter, we demonstrate that Hopf bifurcation will occur when the delay exceeds a critical value. Global existence of bifurcating periodic solutions is established. Numerical simulations supporting the theoretical findings are included. Keywords—Population model; Stability; Hopf bifurcation;...

A symbolic computational technique is used to study the secondary bifurcations of a parametrically excited simple pendulum as an explicit function of the periodic parameter. This is made possible by the recent development of an algorithm which approximates the fundamental solution matrix of linear time-periodic systems in terms of system parameters in symbolic form. By evaluating this matrix at...

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 ...