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On codimensions k immersions of m-manifolds for k=1 and k=m-2
(Springer, 2008-08-01)
Let us consider M a closed smooth connected m-manifold, N a smooth ( 2m-2)-manifold and f: M -> N a continuous map, with m equivalent to 1( 4). We prove that if f*: H(1)(M; Z(2)) -> H(1)(f(M); Z(2)) is injective, then f ...
Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields
(World Scientific Publ Co Pte Ltd, 2015)
Generic bifurcation of refracted systems
(2013-02-05)
In this article we discuss some qualitative and geometric aspects of non-smooth dynamical systems theory. Our goal is to study the diagram bifurcation of typical singularities that occur generically in one parameter families ...
Reversible equivariant Hopf bifurcation
(Springer, 2005-01-01)
In this paper we study codimension-one Hopf bifurcation from symmetric equilibrium points in reversible equivariant vector fields. Such bifurcations are characterized by a doubly degenerate pair of purely imaginary eigenvalues ...
On pairs of regular foliations in R(3) and singularities of map-germs
(Springer, 2008-08-01)
We study germs of pairs of codimension one regular foliations in R(3) . We show that the discriminant of the pair determines the topological type of the pair. We also consider various classifications of the singularities ...
Sliding Vector Fields via Slow-Fast Systems
(Belgian Mathematical Soc Triomphe, 2008-01-01)
This paper concerns differential equation systems on R(n) with discontinuous right-hand sides. We deal with non-smooth vector fields in R(n) having a codimension-one submanifold M as its discontinuity set. After a ...
Bifurcation analysis of a new Lorenz-like chaotic system
(Pergamon-Elsevier B.V. Ltd, 2008-08-01)
In this paper we study the local codimension one and two bifurcations which occur in a family of three-dimensional vector fields depending on three parameters. An equivalent family, depending on five parameters, was recently ...
Bifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor
(Hindawi Publishing Corporation, 2009-01-01)
We study the local codimension one, two, and three bifurcations which occur in a recently proposed Van der Pol-Duffing circuit (ADVP) with parallel resistor, which is an extension of the classical Chua's circuit with cubic ...
DEGENERATE HOPF BIFURCATIONS IN CHUA'S SYSTEM
(World Scientific Publ Co Pte Ltd, 2009-02-01)
In this paper we study the local codimension one, two and three Hopf bifurcations which occur in the classical Chua's differential equations with cubic nonlinearity. A detailed analytical description of the regions in the ...