This paper examines the manner in which heat release resulting from premixed combustion alters the nature of near-critical, axisymmetric, swirling flow in a straight circular pipe. Attention is confined to dilute premixtures so that exothermicity is weak and a small-disturbance approach applicable. The weak exothermicity is found to have a considerably larger effect on the flow. In the absence ...

In recent years the theory of border collision bifurcations has been developed for piecewise smooth maps that are continuous across the border and has been successfully applied to explain nonsmooth bifurcation phenomena in physical systems. However, there exist a large number of switching dynamical systems that have been found to yield two-dimensional piecewise smooth maps that are discontinuou...

This paper introduces a new no–equilibrium chaotic system that is constructed by adding a tiny perturbation to a simple chaotic flow having a line equilibrium. Dynamics of the proposed system are investigated through Lyapunov exponents, bifurcation diagram, Poincaré map and period–doubling route to chaos. A circuit realization is also represented. Moreover, two other new chaotic systems without...

Extended abstract We show that the cusp catastrophe model explains the crash of stock exchanges much better than alternative linear and logistic models. On the data of U.S. stock markets we demonstrate that the crash of October 19, 1987 may be better explained by cusp catastrophe theory, which is not true for the crash of Sept. 11, 2001. With the help of sentiment measures, such as index put/ca...

We study the asymptotic behaviour of the Bianchi type VI0 universes with a tilted γ-law perfect fluid. The late-time attractors are found for the full 7-dimensional state space and for several interesting invariant subspaces. In particular, it is found that for the particular value of the equation of state parameter, γ = 6/5, there exists a bifurcation line which signals a transition of stabili...

Bifurcations of periodic, quasi-periodic and chaotic oscillations are most frequently observed in forced nonlinear circuits containing saturable inductors, whose dynamics are described by nonautonomous di erential equations with periodic external forcing terms. A Poincar e mapping is commonly applied to the study of the bifurcation phenomena. We present some elementary discussion of the codimen...

In this paper, dynamical analysis is presented for a group of unicycles in leader-follower formation. The equilibrium formations were characterized along with the local stability analysis. It was demonstrated that with the variation in control gain, the collective dynamics might undergo Andronov-Hopf and Fold-Hopf bifurcations. An increase in the number of unicycles increase the vigor of quasi-...

Since the pioneering work of Lorenz [1] and Rössler [2], it has been known that chaos can occur in systems of autonomous ordinary differential equations with as few as three variables and one or two quadratic nonlinearities. Many other chaotic systems have been discovered over the last years [3–7]. There have been extensive investigations on dynamical behaviors of these chaotic systems [8–14]. ...

We review some properties of dynamical systems with slowly varying parameters, when a parameter is moved through a bifurcation point of the static system. Bifurcations with a single zero eigenvalue may create hysteresis cycles, whose area scales in a nontrivial way with the adiabatic parameter. Hopf bifurcations lead to the delayed appearance of oscillations. Feedback control theory motivates t...