Hidden attractors in dynamical systems: systems with no equilibria, multistability and coexisting attractors
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[1] P. Grabowski. Absolute stability criteria for infinite-dimensional discrete Lur'e systems with application to loaded distortionless electric RLCG-transmission line , 2013 .
[2] Nikolay V. Kuznetsov,et al. Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation , 2013, NOSTRADAMUS.
[3] Alexander Lanzon,et al. A Robust Kalman Conjecture for First-Order Plants , 2012, ROCOND.
[4] Julien Clinton Sprott,et al. Multistability in a Butterfly Flow , 2013, Int. J. Bifurc. Chaos.
[5] Gennady A. Leonov,et al. Efficient methods in the search for periodic oscillations in dynamical systems , 2010 .
[6] Guanrong Chen,et al. On a Generalized Lorenz Canonical Form of Chaotic Systems , 2002, Int. J. Bifurc. Chaos.
[7] Ricardo Suyama,et al. Chaotic Signals in Digital Communications , 2013 .
[8] Sophie Tarbouriech,et al. Optimization and implementation of dynamic anti-windup compensators with multiple saturations in flight control systems , 2009 .
[9] Johan Grasman,et al. Relaxation Oscillations , 2009, Encyclopedia of Complexity and Systems Science.
[10] G. Leonov,et al. Localization of hidden Chuaʼs attractors , 2011 .
[11] Nikolay V. Kuznetsov,et al. Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems , 2011 .
[12] G. Leonov,et al. Hidden oscillations in dynamical systems , 2011 .
[13] Nikolay V. Kuznetsov,et al. Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor , 2014 .
[14] E. G. Baker,et al. Collection of Short Papers on the Beaver Creek Watershed Study in West Tennessee, 1989-94 , 1995 .
[15] Soumitro Banerjee,et al. Coexisting attractors, chaotic saddles, and fractal basins in a power electronic circuit , 1997 .
[16] Michael I. Gil,et al. Explicit Stability Conditions for Continuous Systems , 2005 .
[17] Nikolay V. Kuznetsov,et al. Hidden attractors in Dynamical Systems. From Hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits , 2013, Int. J. Bifurc. Chaos.
[18] Nikolay V. Kuznetsov,et al. Algorithm for localizing Chua attractors based on the harmonic linearization method , 2010 .
[19] Nikolay V. Kuznetsov,et al. Hidden Oscillations in Aircraft Flight Control System with Input Saturation , 2013, PSYCO.
[20] H. Poincaré,et al. Sur les courbes définies par les équations différentielles(III) , 1885 .
[21] J. Ackermann,et al. Robust Control: The Parameter Space Approach , 2012 .
[22] Awadhesh Prasad,et al. Complicated basins and the phenomenon of amplitude death in coupled hidden attractors , 2014 .
[23] C. A. Desoer,et al. Nonlinear Systems Analysis , 1978 .
[24] Nikolay V. Kuznetsov,et al. A direct method for calculating Lyapunov quantities of two-dimensional dynamical systems , 2011 .
[25] J. A. Tenreiro Machado,et al. Discontinuity and complexity in nonlinear physical systems , 2014 .
[26] Julien Clinton Sprott,et al. Chaotic flows with a single nonquadratic term , 2014 .
[27] Julien Clinton Sprott,et al. A dynamical system with a strange attractor and invariant tori , 2014 .
[28] Steven H. Strogatz,et al. Nonlinear Dynamics and Chaos , 2024 .
[29] Stephen Lynch,et al. Dynamical Systems with Applications using Maple , 2000 .
[30] B. Brogliato,et al. Dissipative Systems Analysis and Control , 2000 .
[31] Ali Abooee,et al. Analysis and circuitry realization of a novel three-dimensional chaotic system , 2013, Commun. Nonlinear Sci. Numer. Simul..
[32] Qingdu Li,et al. On hidden twin attractors and bifurcation in the Chua’s circuit , 2014 .
[33] Nikolay V. Kuznetsov,et al. IWCFTA2012 Keynote Speech I - Hidden attractors in dynamical systems: From hidden oscillation in Hilbert-Kolmogorov, Aizerman and Kalman problems to hidden chaotic attractor in Chua circuits , 2012 .
[34] R Jaimes-Reátegui,et al. Synchronization of chaotic systems with coexisting attractors. , 2006, Physical review letters.
[35] G. Leonov,et al. Hidden attractor in smooth Chua systems , 2012 .
[36] G. Leonov,et al. On stability by the first approximation for discrete systems , 2005, Proceedings. 2005 International Conference Physics and Control, 2005..
[37] A. LeonovG.. Lyapunov quantities , limit cycles and strange behavior of trajectories in two-dimensional quadratic systems , 2008 .
[38] Luca Zaccarian,et al. Anti-windup design for manual flight control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).
[39] Nikolay V. Kuznetsov,et al. Time-Varying Linearization and the Perron Effects , 2007, Int. J. Bifurc. Chaos.
[40] Nikolay V. Kuznetsov,et al. Visualization of Four Normal Size Limit Cycles in Two-Dimensional Polynomial Quadratic System , 2013 .
[41] Zhouchao Wei,et al. Dynamical behaviors of a chaotic system with no equilibria , 2011 .
[42] Michael Margaliot,et al. Absolute stability of third-order systems: A numerical algorithm , 2006, Autom..
[43] E. Lorenz. Deterministic nonperiodic flow , 1963 .
[44] Zhouchao Wei. Complex Dynamics of a New Chaotic System without Equilibria , 2012, 2012 Fifth International Workshop on Chaos-fractals Theories and Applications.
[45] Nikolay V. Kuznetsov,et al. On problems of Aizerman and Kalman , 2010 .
[46] Graham,et al. Nonequilibrium potential for coexisting attractors. , 1986, Physical review. A, General physics.
[47] Nikolay V. Kuznetsov,et al. Algorithm for constructing counterexamples to the Kalman problem , 2010 .
[48] Ulrike Feudel,et al. Complex Dynamics in multistable Systems , 2008, Int. J. Bifurc. Chaos.
[49] Jean-Marc Biannic,et al. Convex Design of a Robust Antiwindup Controller for an LFT Model , 2007, IEEE Transactions on Automatic Control.
[50] Julien Clinton Sprott,et al. Coexistence of Point, periodic and Strange attractors , 2013, Int. J. Bifurc. Chaos.
[51] Mykola Hayvanovych,et al. Algorithms for finding hidden groups and their structure from the streaming communication data , 2009 .
[52] U. Feudel,et al. Control of multistability , 2014 .
[53] Guanrong Chen,et al. A chaotic system with only one stable equilibrium , 2011, 1101.4067.
[54] L. W.,et al. The Theory of Sound , 1898, Nature.
[55] Nikolay V. Kuznetsov,et al. Analytical-numerical methods for investigation of hidden oscillations in nonlinear control systems , 2011 .
[56] Nikolay V. Kuznetsov,et al. Computation of the first Lyapunov quantity for the second-order dynamical system , 2007, PSYCO.
[57] L. Chua,et al. The double scroll family , 1986 .
[58] Irene M. Moroz,et al. Degenerate Hopf bifurcations, hidden attractors, and control in the extended Sprott E system with only one stable equilibrium , 2014 .
[59] Nikolay V. Kuznetsov,et al. Convergence based anti-windup design method and its application to flight control , 2012, 2012 IV International Congress on Ultra Modern Telecommunications and Control Systems.
[60] Stephen P. Timoshenko,et al. Vibration problems in engineering , 1928 .
[61] G. Leonov. Strange attractors and classical stability theory , 2006 .
[62] Maite Grau,et al. Some open problems related to 16 b Hilbert problem , 2003 .
[63] Tao Yang,et al. A SURVEY OF CHAOTIC SECURE COMMUNICATION SYSTEMS , 2004 .
[64] Nikolay V. Kuznetsov,et al. Hidden oscillations in nonlinear control systems , 2011 .
[65] Engelbert Hubbers,et al. A polynomial counterexample to the Markus-Yamabe conjecture , 1997 .
[66] Jinhu Lu,et al. A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.
[67] René Lozi,et al. The Theory of Confinors in Chua's Circuit: accurate Analysis of bifurcations and attractors , 1993, Chua's Circuit.
[68] R.T. Reichert. Dynamic scheduling of modern-robust-control autopilot designs for missiles , 1992, IEEE Control Systems.
[69] Balth. van der Pol Jun.. LXXXVIII. On “relaxation-oscillations” , 1926 .
[70] Tomasz Kapitaniak,et al. Chaotic oscillators : theory and applications , 1992 .
[71] B. R. Andrievskii,et al. Aircraft control with anti-windup compensation , 2012 .
[72] S. E. Khaikin,et al. Theory of Oscillators , 1966 .
[73] Lin Huang,et al. Analysis and Control of Nonlinear Systems with Stationary Sets: Time-Domain and Frequency-Domain Methods , 2009 .
[74] Jibin Li,et al. Hilbert's 16th Problem and bifurcations of Planar Polynomial Vector Fields , 2003, Int. J. Bifurc. Chaos.
[75] Nikolay V. Kuznetsov,et al. Hidden Attractor in Chua's Circuits , 2011, ICINCO.
[76] G. Leonov,et al. Localization of hidden attractors in smooth Chua's systems , 2011 .
[77] René Lozi,et al. THE THEORY OF CONFINORS IN CHUA’S CIRCUIT: ACCURATE ANALYSIS OF BIFURCATIONS AND ATTRACTORS , 1993 .
[78] R. T. Reichert. Dynamic scheduling of modern-robust-control autopilot designs for missiles , 1992 .
[79] P. Neittaanmaki,et al. Drilling systems failures and hidden oscillations , 2012, 2012 IEEE 4th International Conference on Nonlinear Science and Complexity (NSC).
[80] Nikolay V. Kuznetsov,et al. Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor , 2014, Commun. Nonlinear Sci. Numer. Simul..
[81] Nikolay V. Kuznetsov,et al. Algorithm for construction of counterexamples to Aizerman's and Kalman's conjecture , 2010, PSYCO.
[82] Nikolay V. Kuznetsov,et al. Analytical-numerical method for attractor localization of generalized Chua's system , 2010, PSYCO.
[83] Jan Awrejcewicz,et al. Routes to chaos in continuous mechanical systems. Part 1: Mathematical models and solution methods , 2012 .
[84] Leon O. Chua,et al. A zoo of strange attractors from the canonical Chua's circuits , 1992, [1992] Proceedings of the 35th Midwest Symposium on Circuits and Systems.
[85] Zbigniew Galias,et al. Numerical Study of Coexisting attractors for the HéNon Map , 2013, Int. J. Bifurc. Chaos.
[86] X. Liao,et al. Absolute Stability of Nonlinear Control Systems , 2008 .
[87] Bernhard Maschke,et al. Dissipative Systems Analysis and Control , 2000 .
[88] N. Gubar,et al. Investigation of a piecewise linear dynamical system with three parameters , 1961 .
[89] Jaume Llibre,et al. Algebraic determination of limit cycles in a family of three-dimensional piecewise linear differenti , 2011 .
[90] Nikolay V. Kuznetsov,et al. Counterexample of Perron in the Discrete Case , 2001 .
[91] Maciej Ogorzalek. Chaos and Complexity in Nonlinear Electronic Circuits , 1997 .
[92] Nikolay V. Kuznetsov,et al. Limit cycles of quadratic systems with a perturbed weak focus of order 3 and a saddle equilibrium at infinity , 2010 .
[93] Richard M. Murray,et al. Stabilization of integrator chains in the presence of magnitude and rate saturations: a gain scheduling approach , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.
[94] Yang Liu,et al. Intermittent control of coexisting attractors , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[95] Nikolay V. Kuznetsov,et al. Hidden oscillations in stabilization system of flexible launcher with saturating actuators , 2013 .
[96] A three-dimensional singularly perturbed conservative system with symmetry breaking , 2013 .
[97] Nikolay V. Kuznetsov,et al. Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuits , 2011 .
[98] W. Haddad,et al. Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach , 2008 .
[99] Lawrence Markus,et al. Global stability criteria for differential systems. , 1960 .
[100] Julien Clinton Sprott,et al. Simple Chaotic flows with One Stable equilibrium , 2013, Int. J. Bifurc. Chaos.
[101] Roman Senkerik,et al. An investigation on evolutionary reconstruction of continuous chaotic systems , 2013, Math. Comput. Model..
[102] J. J. Stoker. Nonlinear Vibrations in Mechanical and Electrical Systems , 1950 .
[103] J. Sprott,et al. Some simple chaotic flows. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[104] Nikolay V. Kuznetsov,et al. Analytical-Numerical Localization of Hidden Attractor in Electrical Chua’s Circuit , 2013 .
[105] Julien Clinton Sprott,et al. Simple chaotic flows with a line equilibrium , 2013 .
[106] C. Medaglia,et al. A Numerical Study , 2005 .
[107] Nathan van de Wouw,et al. Control of mechanical motion systems with non-collocation of actuation and friction: A Popov criterion approach for input-to-state stability and set-valued nonlinearities , 2009, Autom..
[108] James W. Begun,et al. Chaos and Complexity , 1994 .
[109] I. VagaitsevV.,et al. Localization of hidden Chua ’ s attractors , 2022 .
[110] G. Duffing,et al. Erzwungene Schwingungen bei veränderlicher Eigenfrequenz und ihre technische Bedeutung , 1918 .
[111] O. Rössler. An equation for continuous chaos , 1976 .
[112] Hal R. Varian,et al. Dynamical systems with applications to economics , 2000 .
[113] Guanrong Chen,et al. An Unusual 3D Autonomous Quadratic Chaotic System with Two Stable Node-Foci , 2010, Int. J. Bifurc. Chaos.
[114] K. Fujii,et al. Complexity-stability relationship of two-prey-one-predator species system model: local and global stability. , 1977, Journal of theoretical biology.
[115] Nikolay V. Kuznetsov,et al. Cycles of two-dimensional systems: Computer calculations, proofs, and experiments , 2008 .
[116] Chunlai Mu,et al. Estimations for ultimate boundary of a new hyperchaotic system and its simulation , 2014 .
[117] Julien Clinton Sprott,et al. Cost Function Based on Gaussian Mixture Model for Parameter Estimation of a Chaotic Circuit with a Hidden Attractor , 2014, Int. J. Bifurc. Chaos.
[118] Guanrong Chen,et al. YET ANOTHER CHAOTIC ATTRACTOR , 1999 .
[119] Stephen P. Timoshenko,et al. Vibration Problems in Engineering - fourth edition , 1974 .
[120] Guanrong Chen,et al. Constructing a chaotic system with any number of equilibria , 2012, 1201.5751.
[121] S. Nikravesh. Nonlinear Systems Stability Analysis: Lyapunov-Based Approach , 2013 .
[122] F. Tricomi,et al. Integrazione di un' equazione differenziale presentatasi in elettrotecnica , 1933 .