Complex dynamics in the reduced swing equations of a power system are investigated. As the change of bifurcation parameter μ, the system exhibits complex bifurcations, such as saddle-node bifurcation, Hopf bifurcation, cyclic fold bifurcation and torus bifurcations and complex dynamics, such as periodic orbits, quasiperiodic orbits, period-doubling orbits and chaotic attractors which link with ...

By using Sherman-Morrison-Woodbury formula, we introduce a preconditioner based on parameterized splitting idea for generalized saddle point problems which may be singular and nonsymmetric. By analyzing the eigenvalues of the preconditioned matrix, we find that when α is big enough, it has an eigenvalue at 1 with multiplicity at least n, and the remaining eigenvalues are all located in a unit c...

This paper studies the projected saddle-point dynamics associated to a convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and (projected) gradient ascent in variables corresponding to concavity. We examine the role that the local and/or global nature of the convexity-concavity propertie...

In this paper we demonstrate that valley-ridge inflection (VRI) points of a potential energy surface (PES) have dynamical influence on the fate trajectories underlying Hamiltonian system. These attracted attention chemists in past decades when studying selectivity problems organic chemical reactions whose landscape exhibits post-transition-state bifurcation region between two sequential saddles...

Tonically spiking as well as bursting neurons are frequently observed in electrophysiological experiments. The theory of slow–fast dynamical systems can describe basic scenarios of how these regimes of activity can be generated and transitions between them can be made. Here, we suggest a biophysically plausible mechanism based on homoclinic bifurcations of a saddle periodic orbit which explains...

We study the behavior of reacting tracers in a chaotic flow. In particular, we look at an autocatalytic reaction and at a bistable system which are subjected to stirring by a chaotic flow. The impact of the chaotic advection is described by a one-dimensional phenomenological model. We use a nonperturbative technique to describe the behavior near a saddle node bifurcation. We also find an approx...

In this work, we find the results for folded part projection of butterfly catastrophe model onto control space, using methods from theory to obtain stability and catastrophic behavior finite periodic solutions some non-linear differential equations. Finally, have shown that a saddle-node bifurcation, which can be classified as mutation, accompanies surface folding.

We demonstrate numerically calculated electromagnetic eigenmodes of a 3D dome cavity resonator that owe their shape and character entirely to the Goos-Hänchen effect. The V-shaped modes, which have purely TE or TM polarization, are well described by a 2D billiard map with the Goos-Hänchen shift included. A phase space plot of this augmented billiard map reveals a saddle-node bifurcation; the st...