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SHILNIKOV BIFURCATION: STATIONARY QUASI-REVERSAL BIFURCATION
(WORLD SCIENTIFIC PUBL CO PTE LTD, 2008-07)
A generic stationary instability that arises in quasi-reversible systems is studied. It is characterized by the confluence of three eigenvalues at the origin of complex plane with only one eigenfunction. We characterize ...
NONDEGENERATE UMBILICS, THE PATH FORMULATION and GRADIENT BIFURCATION PROBLEMS
(World Scientific Publ Co Pte Ltd, 2009-09-01)
Parametrized contact-equivalence is a successful theory for the understanding and classification of the qualitative local behavior of bifurcation diagrams and their perturbations. Path formulation is an alternative point ...
3-Dimensional hopf bifurcation via averaging theory
(2007-03-01)
We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br ...
3-Dimensional hopf bifurcation via averaging theory
(2007-03-01)
We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br ...
Integration-Free analysis of nonsmooth local dynamics in planar filippov systems
(WORLD SCIENTIFIC PUBL CO PTE LTD, 2009-03-01)
In this paper, we present a novel method to analyze the behavior of discontinuous piecewise-smooth autonomous systems (denominated Filippov systems) in the planar neighborhood of the discontinuity boundary (DB). The method ...
Detection of limit cycle bifurcations using harmonic balance methods
(World Scientific, 2004-12)
In this paper, bifurcations of limit cycles close to certain singularities of the vector fields are explored using an algorithm based on the harmonic balance method, the theory of nonlinear feedback systems and the monodromy ...
Bifurcation theory applied to the analysis of power systems
(Unión Matemática Argentina, 2008-12)
In this paper, several nonlinear phenomena found in the study of power system networks are described in the context of bifurcation theory. Toward this end, a widely studied 3-bus power system model is considered. The ...
NONDEGENERATE UMBILICS, THE PATH FORMULATION and GRADIENT BIFURCATION PROBLEMS
(World Scientific Publ Co Pte Ltd, 2014)