Hopf Bifurcations in a Watt Governor with a Spring

This paper pursues the study carried out in [ 10], focusing on the codimension one Hopf bifurcations in the hexagonal Watt governor system. Here are studied Hopf bifurcations of codimensions two, three and four and the pertinent Lyapunov stability coefficients and bifurcation diagrams. This allows to determine the number, types and positions of bifurcating small amplitude periodic orbits. As a consequence it is found an open region in the parameter space where two attracting periodic orbits coexist with an attracting equilibrium point.

Bifurcation analysis of a model for biological control

In this paper we study the Lyapunov stability and Hopf bifurcation in a biological system which models the biological control of parasites of orange plantations. (c) 2007 Elsevier Ltd. All rights reserved.

Stability and Hopf bifurcation in an hexagonal governor system

In this paper we study the Lyapunov stability and the Hopf bifurcation in a system coupling an hexagonal centrifugal governor with a steam engine. Here are given sufficient conditions for the stability of the equilibrium state and of the bifurcating periodic orbit. These conditions are expressed in terms of the physical parameters of the system, and hold for parameters outside a variety of codimension two. (C) 2007 Elsevier Ltd. All rights reserved.

Solvatochromic and lonochromic Effects of Iron(II)bis-(1,10-phenanthroline)dicyano: a Theoretical Study

Solvatochromic and ionochromic effects of the iron(II)bis(1,10-phenanthroline)dicyano (Fe(phen)(2)(CN)(2)) complex were investigated by means of combined DFT/TDDFT calculations using the PBE and B3LYP functionals. Extended solvation models of Fe(phen)(2)(CN)(2) in acetonitrile and aqueous solution, as well as including interaction with Mg(2+), were constructed. The calculated vertical excitation energies reproduce well the observed solvatochromism in acetonitrile and aqueous solutions, the ionochromism in acetonitrile in the presence of Mg(2+), and the absence of ionochromic effect in aqueous solution. The vertical excitation energies and the nature of the transitions were reliably predicted after inclusion of geometry relaxation upon aqueous micro- and global solvation and solvent polarization effect in the TDDFT calculations. The two intense UV-vis absorption bands occurring for all systems studied are interpreted as transitions from a hybrid Fe(II)(d)/cyano N(p) orbital to a phenanthroline pi* orbital rather than a pure metal-to-ligand-charge transfer (MLCT). The solvatochromic and ionochromic blue band shifts of Fe(phen)(2)(CN)(2) were explained with preferential stabilization of the highest occupied Fe(II)(d)/cyano N(p) orbitals as a result of specific interactions with water solvent molecules or Mg(2+) ions in solution. Such interactions occur through the CN(-) groups in the complex, and they have a decisive role for the observed blue shifts of UV-vis absorption bands.