Imperfection sensitivity properties are derived for finite dimensional elastic conservative systems exhibiting hill-top branching at which arbitrary many bifurcation points coincide with a limit point. The critical load at a hill-top branching point is demonstrated to be insensitive to initial imperfections when all the bifurcation points are individually symmetric. Therefore, it is not dangero...

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich. The neural system exhibits a unique rest point or three ones for the different values of coupling strength by employing t...

The bifurcation diagram for the buckling of a planar elastica under a load λ is made up of a “trivial” branch of unbuckled configurations for all λ and a sequence of branches of buckled configurations that are connected to the trivial branch at pitchfork bifurcation points. We use several perturbation expansions to determine how this diagram perturbs with the addition of a small intrinsic shape...

We describe the qualitative dynamics and bifurcation set for a laser with injected signal for small cavity detunings. The main organizing center is the Hopf-saddle-node bifurcation from where a secondary Hopf bifurcation of a periodic orbit originates. We show that the laser’s stable cw solution existing for low injections, also suffers a secondary Hopf bifurcation. The resonance structure of b...

Periodic solutions of certain large scale systems of ODEs can be computed eeciently using a hybrid Newton-Picard scheme, especially in a continuation context. In this paper we describe and analyse a numerical method to accurately compute period doubling bifurcation points using the Newton-Picard approach. The method avoids the computation of the full monodromy matrix, which is present in the de...

The smart OGY control method is proposed for two-link rigid robot arm. For this goal the Bifurcation diagram should be applied for acceptable wide range of the input amplitude. Then by using the robot arm in a chaotic amplitude range and Poincare section, the UPO's will be found. After that, the OGY rules are defined for each UPO's and the maximum changed value of amplitude for each UPO's, whic...

Distinguishing the stability of characteristic curves for nonlinear resistive circuits is requirement and importance to design various electronic circuit exactly. Since every resistive element has a parasitic component, solutions on the characteristic curves are stable or unstable. In this paper, we show that the stability will be mainly changed at the bifurcation points such as limit point and...

The objective of this work was to investigate the dynamics host–parasitoid model with spatial refuge effect. For this, two discrete models were considered under Suppose that a constant population hosts may seek and protection from an attack parasitoids. We found parametric factors affecting existence equilibrium points uniqueness points. A local stability analysis also carried out. Bifurcation ...

This paper presents a detailed bifurcation analysis of multi-parameter power systems. Equilibrium points are used to evaluate the system eigenvalues and obtain different bifurcation diagrams for two sample systems. The paper studies the influence of hard-limits, AVR droop and reactive power compensation on the local bifurcations of the test systems, using detailed generator models. The stabili...

The coalescence of a Hopf bifurcation with a codimension-two cusp bifurcation of equilibrium points yields a codimension-three bifurcation with rich dynamic behavior. This paper presents a comprehensive study of this cusp-Hopf bifurcation on the three-dimensional center manifold. It is based on truncated normal form equations, which have a phase-shift symmetry yielding a further reduction to a ...