Stability calculations for piecewise-smooth delay equations [PDF]
, 2008 This paper describes a new method for computing the stability of nonsmooth periodic orbits of piecewise-smooth dynamical systems with delay. Stability computations for piecewise-smooth dynamical systems without delay have previously been performed using ...
Barton, DAW
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Stability and regulation of nonsmooth dynamical systems [PDF]
, 2004 The mathematical analysis of nonsmooth Lagrangian dynamical systems leads to introduce mathematical tools which are unusual in control theory, velocities with locally bounded variations, measure accelerations, measure differential inclusions to name a ...
Chareyron, Sophie, Wieber, Pierre-Brice
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Arnol′d tongues arising from a grazing-sliding bifurcation [PDF]
, 2009 The Neımark–Sacker bifurcation, or Hopf bifurcation for maps, is a well-known bifurcation for smooth dynamical systems. At this bifurcation a periodic orbit loses stability, and, except at certain “strong” resonances, an invariant torus is born.
Osinga, HM +3 more
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The two-fold singularity of discontinuous vector fields [PDF]
, 2009 When a vector field in 3 dimensions is discontinuous on a smooth codimension one surface, it may be simultaneously tangent to both sides of the surface at generic isolated points (singularities).
M. R. Jeffrey +4 more
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Lower semicontinuity of attractors for non-autonomous dynamical systems [PDF]
, 2009 This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic
Langa, José A. +3 more
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Bifurcations of piecewise smooth flows:perspectives, methodologies and open problems [PDF]
, 2012 In this paper the theory of bifurcations in piecewise smooth flows is critically surveyed. The focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting significant areas where a detailed understanding is presently lacking ...
A. Colombo +10 more
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Isochronous Attainable Manifolds for Piecewise Smooth Dynamical Systems [PDF]
, 2021 Considering the concept of attainable sets for differential inclusions, we introduce the isochronous manifolds relative to a piecewise smooth dynamical systems in R-2 and R-3, and study how analytical and topological properties of such manifolds are ...
Difonzo, Fabio V.
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Two-folds in nonsmooth dynamical systems [PDF]
, 2009 In a three dimensional dynamical system with a discontinuity along a codimension one switching manifold, orbits of the system may be tangent to both sides of the switching manifold generically at isolated points.
Mike R Jeffrey, Jeffrey, Mike R
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Input-to-state stability for discrete-time time-varying systems with applications to robust stabilization of systems in power form [PDF]
, 2005 Input-to-state stability (ISS) of a parameterized family of discrete-time time-varying nonlinear systems is investigated. A converse Lyapunov theorem for such systems is developed.
Laila, D. S. +5 more
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Sliding bifurcations and non-determinism in systems with switching [PDF]
, 2011 Dynamical events associated with loss of determinacy in piecewise-smooth dynamical systems are reviewed. The causes of non-determinacy are discussed, and the conditions for their occurence in general systems are derived. These events can be characterized
Mike R Jeffrey, Jeffrey, Mike R
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