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Compartimos referencias relacionadas directa o indirectamente con sistemas dinámicos modelados mediante sistemas de ecuaciones diferenciales definidos por tramos (en ingl. se incluye p. ej. PSS, PWL, PWA Systems). Se indican también algunas referencias contextuales.
[Rev. 2017.04.22 ]
Papers
∃Alzate Castaño, Ricardo (2008) Analysis and application of bifurcations in systems with impact and chattering . PhD Dissertation.{Tutor: Prof. Mario di Bernardo} [acc. 2014.12.25]
Barton , David A. W. (2009) Stability calculations for piecewise-smooth delay equations , International Journal of Bifurcation and Chaos , vol 19., pp. 639-650 [acc. 2014.01.08]
Benmerzouk , Djamila & Jean-Pierre Barbot .(2009)Chaotification of piecewise smooth systems . Chaos 09, Londre, United Kingdom. <hal-00772236> [acc. 2014.12.25]
τBiemond , J. J. B. et al. (2009) A complete bifurcation analysis of planar conewise affine systems . [acc. 2014.10.12]
τBiemond , J. J. B. et al. (2010) Nonsmooth bifurcations of equilibria in planar continuous systems. Nonlinear Analysis: Hibrid systems 4, 451-474. Elsevier {∃see procedure in section 4.3} [acc. 2014.09.15]
Brandon , Quentin (2009) →Numerical Method of Bifurcation Analysis for Piecewise-smooth Nonlinear Dynamical Systems . Tesis Doctoral {ver también: ⇒Numerical Method of Bifurcation Analysis for Piecewise-smooth Nonlinear Dynamical Systems: Application to Alpazur oscillator }[acc. 2014.01.08]
Broucke , Mireille E. et al. (2001) Structural stability of piecewise smooth systems . [acc. 2014.01.08]
Burden , Samuel A. et al. (2013) Model reduction near periodic orbits of hybrid dynamical systems . [acc. 2015.01.16]
ℵBurden , Samuel A. et al. (2014) Event–Selected Vector Field Discontinuities Yield Piecewise–Differentiable Flows . [acc. 2014.12.25]
τℵCarmona Centeno, Victoriano (2002) Bifurcaciones en sistemas dinámicos lineales a trozos . Tesis doctoral. Univ. de Sevilla, España [2015.04.21]
∃Champnewys , Alan R, Mario di Bernardo (2008) Piecewise smooth dynamical systems . Scholarpedia 3(9):4041 [acc, 2014.12.25]
∀Champneys , Alan (2009) Rock, Rattle and Slide bifurcation theory for piecewise-smooth systems . [acc. 2014.12.25]
Colombo , A. et al. (2009) Stable Manifolds of Saddles in Piecewise Smooth Systems . CMES, vol.53, no.3, pp.235-254 [acc. 2014.01.08]
Colombo , A. et al. (2010) ♦Teixeira singularities in 3D switched feedback control systems . Systems & Control Letters, 59 (10). pp. 615-622 [acc. 2014.01.08]
Colombo , A. et al. (2012) ♦Bifurcations of piecewise smooth flows: Perspectives, methodologies and open problems . Physica D 241 (2012) 1845–1860 Elsevier [acc. 2014.01.08]
Dercole , Fabio, et al. (2007) Bifurcation analysis of piecewise smooth ecological models . Theoretical Population Biology 72 (2007) 197–213 [acc. 2014.10.31]
di Bernardo , Mario et al. (2000) Unified derivation of normal form maps for grazing bifurcations in n-dimensional piecewise dynamical systems . [acc. 2015.01.16]
di Bernardo , Mario (2008) Discontinuity-induced Bifurcations of Equilibria in piecewise-smooth systems .CDS08 Monopoli [acc. 2014.12.25]
di Bernardo , Mario (2008) Discontinuity-induced Bifurcations of Limit Cycles in piecewise-smooth systems .CDS08 Monopoli [acc. 2014.01.09]
di Bernardo , Mario et al. (2008) Bifurcations in Nonsmooth Dynamical Systems . SIAM Reviews Vol. 50, No. 4, pp. 629–701. [acc. 2014.01.08]
∃di Bernardo , Mario & S. J. Hogan (2010) Discontinuity-induced bifurcations of piecewise smooth dynamical systems . Phil. Trans. R. Soc. A (2010) 368, 4915–4935 [acc. 2014.12.25]
∀di Bernardo , Mario (2011) ⇒Adaptive Control and Synchronization of PWS systems and networks . ISCDE, Batz-sur-Mer. [acc. 2014.10.31]
∀Dieci , Luca & Luciano Lopez (2009) →Fundamental matrix solutions of piecewise smooth differential systems . {Draft} {ver también: Mathematics and Computers in Simulation 81 (2011) 932–953 ⇒ScienceDirect MATCOM paper , (contiene link a PDF)} [acc. 2014.01.08]
Doede l, Eusebius (2010) →Lecture Notes on Numerical Analysis of Nonlinear Equations . [acc. 2014.01.08]
Elmegårt , M. et al. (2013) Bifurcation analysis of a smoothed model of a forced impacting beam and comparison with an experiment . Arxiv [acc. 2014.01.08]
ℵτFernandez-García , Soledad (2012) Bifurcaciones de Órbitas Periódicas y Conjuntos Invariantes en Sistemas Dinámicos Lineales a Trozos . Tesis Doctoral, Univ. de Sevilla [acc. 2015.04.10]
ℵFerrer , J. et al. (2011) Unobservable Planar Bimodal Linear Systems: Miniversal Deformations, Controllability and Stabilization .
Preprint [acc. 2017.04.22]
ℵFerrer , J. et al. (2013) Structural Stability of Planar Bimodal Linear Systems .
11th International Conference of Numerical Analysis and Applied Mathematics 2013 AIP Conf. Proc. 1558, 2205-2208 [acc. 2017.04.22]
λGalias , Z. (2011) On rigorous integration of piece-wise linear systems . [acc. 2014.11.18]
ℵτGarcía-Medina , Elisabeth (2012) Conexiones Globales y Comportamientos Periódicos en Sistemas Dinámicos Lineales a Trozos . Tesis Doctoral. Univ. de Sevilla [acc. 2015.04.10]
ℵτGarcía-Medina , Elisabeth (2012) “Existence of global connections in three-dimensional piecewise linear systems “. [acc. 2015.03.23]
Gardini , Laura & Fabio Tramontana (2012) Structurally unstable regular dynamics in 1D piecewise smooth maps, and circle maps . Chaos, Solitons & Fractals 45 (2012) 1328–1342, Elsevier [acc. 2014.01.08]
τGranados , A et al. (2012) The Melnikov method and subharmonic orbits in a piecewise smooth system . Arxiv. [acc. 2014.09.15]
∑τGranados , A et al. (2012) Local and global phenomena in piecewise-defined systems: from big bang bifurcations to splitting of heteroclinic manifolds . {Tesis} [acc. 2014.10.12]
Hogan , John (2012) ∑Piecewise smooth dynamical systems . Dynamical Systems: 100 years after Poincaré. Gijón, Spain [acc. 2014.01.10]
τ²Ivanov , Alexander P. (2012) Analysis of discountinuous bifurcations in nonsmooth dynamical systems . [acc. 2015.01.21]
Jacquemard , Alain et al. (2012) Stability conditions in piecewise smooth dynamical systems at a two-fold singularity . [acc. 2014.01.08]
Jeffrey , M. R & A. Colombo (2009) The Two-Fold Singularity of Discontinuous Vector Fields . SIAM J. Applied Dynamical Systems, Vol. 8, No. 2, pp. 624–640 [acc. 2014.01.09]
λKersing , Stefan & Martin Buss (2014) Adaptive identification of continuous-time switched linear and piecewise linear systems . [acc. 2014.11.18]
Kristiansen , K. U. & J. Hogan (2014) On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems en . [acc. 2014.11.30]
ℵKuznetson , Yu A. (2000) Lecture Notes of Numerical Bifurcation Analysis : [acc. 2014.12.13 ]
[L1] ⇒Continuation problems. Numerical continuation of equilibria and limit cycles of ODEs .
[L2] ⇒Equilibrium bifurcations of ODEs and their numerical analysis .
[L3] ⇒Bifurcations of limit cycles of ODEs and their numerical analysis using BVPs .
[L4] ⇒Numerical local bifurcation analysis of iterated maps .
[L5] ℵ ⇒Numerical continuation of connecting orbits of iterated maps and ODEs .
Kuznetsov , Yu A. et al. (2003) ♦One-parameter bifurcations in planar Filippov systems . International Journal of Bifurcation and Chaos, Vol. 13, No. 8 (2003) 2157-2188 [acc. 2014.01.08]
Leine , R. I. (2006) Bifurcations of equilibria in non-smooth continuous systems . Physica D 223 (2006) 121–137 [acc. 2014.01.09]
ℵτLlibre , Jaime; Ponce , Enrique; Torres , Francisco (2009) Dos bifurcaciones de ciclos límite en sistemas lineales a trozos en . [acc. 2015.04.10]
∏τMezic , I., Stephen Wiggins (1999) A method for visualization of invariant sets of dynamical systems based on the ergodic partition . Chaos 9:1 [acc. 2014.10.12]
τPonce , E. (2012) Piecewise Linear Systems: twenty years on . [acc. 2015.04.09]
τPonce , E. (2014) Bifurcations in piecewise linear systems: case studies . MAT70 An international conference on dynamical systems in honor of the 70th birthday of Marco Antonio Texeira. Notes of a Mini-course held at IMECC, Campinas, São Paulo. [acc, 2014.10.12]
Russo , Giovanni & Marco di Bernardo (2011) On Contraction of Piecewise Smooth Dynamical Systems . Preprints of the 18th IFAC World Congress Milano (Italy) August 28 – September 2, 2011 [acc. 2014.01.08]
Salinas-Varela , Adrián A. et al. (2009)Analysis of piecewise linear (PWL) feedback systems . [acc. 2014.11.18]
Sieber , J. & P. Kowalczyk (2010) Small-scale instabilities in dynamical systems with sliding . Arxiv. [acc. 2014.01.09]
Simpson , D. J. W. & R. Kuske (2012) Stochastically Perturbed Sliding Motion in Piecewise-Smooth Systems . Arxiv [acc. 2014.01.09]
ℵSimpson , D.J.W. & J. D. Meiss (2007) Andronov–Hopf bifurcations in planar, piecewise-smooth, continuous flows [acc. 2014.12.23]
ℵSimpson , D.J.W. & J. D. Meiss (2010) Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems [acc. 2014.12.23]
ℵSvahn , Fredrik (2009) On the stability and control of piecewise-smooth dynamical systems with impacts and friction . Doctoral Thesis. [acc. 2014.01.08]
ℵSzalai , Róbert, et al. (2008) Arnold’s tongues arising from a grazing-sliding bifurcation of a piecewise-smooth system . [acc. 2014.12.25]
∑τWarwick , D. J. (2010) Fundamentals of Piecewise-Smooth Continuous Systems . {Book chapter} [acc. 2014.10.12]
ℵXu , Bin et al. (2013) Homoclinic bifurcations in planar piecewise-linear systems . Discrete Dynamics in Nature and Society, Vol. 2013 [acc. 2014.12.23]
Yang , Xiao-Song et al. (c. 2008) Existence and bifurcation of homoclinic orbits in planar piecewise linear systems . Arxiv [acc. 2014.01.08]
People
Places
Applied Nonlinear Mathematics . University of Bristol
Dance-Net . Coordinadores Lluís Alsedà (UAB) y Enrique Ponce (US)
Events
Tools
AUTO
[Comercial ] Phaser: a universal simulator for dynamical systems
τDe Witte , V et al. (2012) Interactive initialization and continuation of homoclinic and heteroclinic orbits in Matlab . ACM Transactions of Mathematical Software 38 (3) art. 18 [acc. 2014.09.15]
Context
∃Abraham , Frederick D., Ralph H. Abraham, Christopher D. Shaw (1990) Basic principles of dynamical systems . Book chapter (3). [acc. 2015.01.14]
§Acary , Vincent, et al. (2009) Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics , Springer Verlag, 35, pp.526, 2008, Lecture Notes in Applied and Computational Mechanics, 978-3-540-75391-9. [acc. 2015.02.25]
§Arango , Ivan et al. (2011) Localización de bifurcaciones deslizantes en un oscilador rotativo de doble leva . Dyna, vol. 78, núm. 167, 2011, pp. 160-168, Universidad Nacional de Colombia [acc. 2015.02.25]
Aubin , David (2004) Forms of Explanations in the Catastrophe Theory of René Thom: Topology, Morphogenesis, and Structuralism . Growing Explanations: Historical Perspective on the Sciences of Complexity, ed. M. N. Wise, Durham: Duke University Press, 2004, 95-130. [acc. 2014.01.09]
Awrejcewics , Jan et al. (2013) Dynamical systems applications . {Libro }[acc. 2014.11.30]
Benadero , Luis et al. (2014) Resonances in an area preserving continuous piecewise linear map . [acc. 2015.01.16]
ℵBeyn Wolf-Jürgen, et al. (2000) Numerical continuation and computation of normal forms . [acc. 2014.12.13]
∀Broucke , Mireille R. et al. (2001) Structural stability of piecewise smooth systems . [acc. 2015.01.14]
Calleja , R. C., et al. (2012) Boundary-value problem formulation for computing invariant manifolds and connecting orbits in the circular restricted three body problem. [acc. 2014.10.14]
∏Castelli , Roberto et al. (2014) Parameterization of invariant manifolds for periodic orbits (I): efficient numerics via the Floquet normal form . [acc. 2014.12.29]
ℵ Castillo , Zenaida (2004) A New Algorithm for Continuation and Bifurcation Analysis of Large Scale Free Surface Flows . PhD Dissertation, Rice Univ. [acc. 2014.12.23]
∏Cliffe , K. A. et al.) (2008) The numerical analysis of bifurcation problems with applications to fluid mechanics . Acta Numerica (2008) pp. 39-131. [acc. 2014.11.09]
§Davis , K. E. et al. (2010) The use of invariant manifolds for transfers between unstable periodic orbits of different energies . Celest. Mech. Astr. 107: 471-485 [acc. 2014.10.14]
∏Day , S. et al. (2004) A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems . SIAM J. APPLIED DYNAMICAL SYSTEMS Vol. 3, No. 2, pp. 117–160. [acc. 2014.12.02]
ℵ² Dijkstra , H. A. et al. (2014) Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation . [acc. 2014.12.23]
∏Dellnitz , M. et al. (2010) The numerical detection of connecting orbits . [acc. 2014.10.12]
∏Dellnitz , M. et al. (2010) The algorithms behind GAIO: Set oriented numerical methods for dynamical systems . In Bernold Fiedler, editor, Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems , pages 145-174, Springer 2001 [acc. 2014.11.30]
τElhadj , Z. & Sprott, J. C. (2012) Non-existence of the Shilnikov chaos in continuous-time systems . Appl. Math. Mech -English Ed. 33(3)1-4 [acc. 2014.11.17]
§Escobar Callejas , Carlos (2013) Contribución al estudio de los sistemas no suaves (bifurcación Zip) . Tésis, Doctorado en Ingeniería. Univ. Nacional de Colombia. [acc. 2015.02.25]
Feng . B., R. Hu (2003) A survey of homoclinic and heteroclinic orbits . [acc. 2014.10.14]
∑Fring , Andreas (2009) Dynamical systems . Lecture Notes. City Univ. of London [acc. 2014.12.22]
∇Fuhrmann , Anton et al. (1997) Collaborative augmented reality: exploring dynamical systems . [acc. 2015.01.14]
∇Gasull , A. & H. Giacomini, J. Torregrosa . (2010) Some results on homoclinic and heteroclinic connections in planar systems .
Nonlinearity, 23, 2977–3001, 2010. [acc. 2014.12.25]
Glasner , Eli, & Benjamin Weiss (1998) Sensitive dependence on initial conditions . [acc. 2014.12.30]
∏Guckenheimer , J., A. Vladimirsky (2002+) A fast method for approximating invariants manifolds . [acc. 2014.10.14]
∇Gutschke , Martin et al. (2014) Differential geometric methods for examining the dynamics of slow-fast vector fields . Springer. [acc. 2015.01.14]
φHasselblatt , B.; Y. Pesin (2005) Partially hyperbolic dynamical systems . [acc. 2014.11.30]
Homburg , A. J., B. Sandstede (2010) Homoclinic and heteroclinic bifurcations in vector fields . [acc. 2014.10.14]
φHurder , Steven (2014) Lectures on foliation dynamics: Barcelona 2014 . [acc. 2014.11.30]
∞Jiang , Qibao; Llibre , Jaume (2005) Qualitative Classification of Singular Points . Qualitative Theory of Dynamical Systems 6, 87-167 [acc. 2014.02.23]
⇒Khang , Byungik (2009) Redefining Chaos: Devaney-chaos for Piecewise Continuous Dynamical Systems . International Journal of Mathematical Methods in Applied Sciences, Vol. 3, Issue 4 [acc. 2014.01.09]
Khang , Byungik, et al. (2014) Sliding Singularities of Bounded Invertible Planar Piecewise Isometric Dynamics . Int’l J. of Math. Models and Methods in Applied Sciences, Vol. 8. [acc. 2014.11.27]
∀Knill , Oliver (1993) Spectral, ergodic and cohomological problems in dynamical systems . PhD Dissertation. [acc. 2014.12.30]
§Koon , W. S., et al. (2010) Heteroclinic connections between periodic orbits and resonant transitions in celestial mechanics . [acc. 2014.10.14]
Kuehn , Christian (2011) A Mathematical Framework for Critical Transitions: Bifurcations, Fast-Slow Systems and Stochastic Dynamics [acc. 2014.11.18]
∀Kumar , Vijay & Peng Song (2003) Geometric theory of dynamical systems . Course notes. Univ. of Pennsylvania. [acc. 2015.01.14]
∏Lessard , J-P., et al. (2014) Computer assisted proof of transverse saddle-to-saddle connecting orbits for first order vector fields . [acc. 2014.10.14]
∏Levnajiv , Z., Igor Mezic . (2010) Ergodic theory and visualization I: Mesochronic Plots for Visualization of Ergodic Partition and Invariant Sets . Arxiv. [ac. 2014.10.12]
∏Levnajiv , Z., Igor Mezic . (2014) Ergodic theory and visualization II: Harmonic meshochronic plots visualize (quasi)periodic sets . Arxiv. [acc. 2014.10.12]
∞Liu , Xianping (1999) Symbolic tools for the analysis of nonlinear dynamical systems . [acc. 2014.02.23]
∏Liu , Y. et al. (1994) The numerical computation of connecting orbits in dynamical systems: a rational spectra approach . J. of Computational Physics 111:2 [acc. 2014.10.12]
ℵ Lu , James, et al. (2006) Inverse bifurcation analysis: application to simple gene systems . Algorithms for Molecular Biology 2006, 1:11 [acc. 2014.12.23]
βMarsden , Jerrold E. (2009) Basic Theory of Dynamical Systems .{⇒Lecture Notes CDS140-2009 }[acc. 2014.12.24]
∑Makarenkov , Oleg & Jeroen S. W. Lamb (2011) Dynamics and bifurcations of nonsmooth systems: a survey . [acc. 2015.01.17]
ℵ²Meijer , Hil et al. (c. 2006) ⇒Numerical bifurcation analysis . [acc. 2014.12.13]
∏Mireles-James , J. D.& Héctor Lomelí (2010) Computation of Heteroclinic Arcs with application to the Volume Preserving Hénon Family . SIAM J. Applied Dynamical Systems, Vol. 9, No. 3 pp. 919-953 [acc. 2014.12.29]
ℵMorrison , Tina Marie (2006) Three problems in nonlinear dynamics with 2:1 parametric excitation . PhD Dissertation. [acc. 2014.12.21]
Nersesov , Sergey C. & Wassim. M. Haddad (2006) On the stability and control of nonlinear dynamical systems via vector Lyapunov functions . [acc. 2015.01.14]
ℵOsorio , G (2007 Complex behavior in impacting systems . PhD Dissertation. Univ. of Naples Federico II. [acc. 2014.12.19]
φPrabhakar G. Vaidya; Swarnali Majumder (2011) Modifying some foliated dynamical systems to guide their trajectories to specified sub-manifolds .
∞Ravnås , Eirik (2008) Continuation and Bifurcation software in MATLAB . Thesis (Master of Science in Physics and Engineering) NTNU. [acc. 2014.03.01]
§Ruiz Arenas , Ana Catalina (2013) Análisis de sistemas no suaves utilizando el método SPT . Tésis Magister de Ing., Univ. EAFIT, Medellín, Colombia [acc. 2015.02.25]
∏²Reinhardt , Christian P. (2013) Validated computation of connecting orbits in ordinary differential equations . PhD Dissertation [acc. 2014.12.29]
∏Sandri , Marko (1996) Numerical calculation of Lyapunov exponents . Mathematica Journal vol. 6, issue 3 [acc. 2014.12.22]
∞Seydel , R. (2001) Assessing voltage collapse . LAAR 31,3 pp. 171-176 [acc. 2014.03.01]
ℵShilnikov , Leonid (1997) Mathematical problems in nonlinear dynamics: a tutorial [acc. 2014.12.21]
Smale , S. (1967) Differentiable dynamical systems . Bull. A.M.S. v. 73, 747-817. [acc. 2014.12.22]
∏Spence , Alastair & Ivan C. Graham (2002) Numerical methods for bifurcation problems . [acc. 2014.11.09]
∏Stuart , A. M. (1994) Numerical analysis of dynamical systems . Acta Numerica [acc. 2014.10.12]
∂Teixeira , Marco Antonio (2008)Perturbation theory for non-smooth systems . [acc. 2015.01.19]
Tsatsanis , Peter (2012) On René Thom’s Significance for Mathematics and Philosophy . Scripta Philosophiæ Naturalis 2: 213-229. [acc. 2014.12.20]
Zou , Yongkui et al. (2003) Generalized Hopf bifurcation for non-smooth planar dynamical systems . [acc. 2015.01.16]
∏Zhou , T. et al. (2005) An algorithm for computing heteroclinic orbits and its application to chaos synthesis in the generalized Lorenz system. [acc. 2014.10.14]
Normal Forms (selected)
Moduli spaces connection
Libros selectos (de libre acceso)