Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion

[1]  Nikolay V. Kuznetsov,et al.  Hidden attractor in the Rabinovich system, Chua circuits and PLL , 2016 .

[2]  Nikolay V. Kuznetsov,et al.  Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity , 2015, Commun. Nonlinear Sci. Numer. Simul..

[3]  Nikolay V. Kuznetsov,et al.  Coincidence of the Gelig–Leonov–Yakubovich, Filippov, and Aizerman–Pyatnitskiy definitions , 2015 .

[4]  Nikolay V. Kuznetsov,et al.  Limitations of the classical phase-locked loop analysis , 2015, 2015 IEEE International Symposium on Circuits and Systems (ISCAS).

[5]  Nikolay V. Kuznetsov,et al.  A short survey on nonlinear models of the classic Costas loop: Rigorous derivation and limitations of the classic analysis , 2015, 2015 American Control Conference (ACC).

[6]  Awadhesh Prasad,et al.  Controlling Dynamics of Hidden Attractors , 2015, Int. J. Bifurc. Chaos.

[7]  T. N. Mokaev,et al.  Localization of a hidden attractor in the Rabinovich system , 2015 .

[8]  G. A. Leonov,et al.  Estimation of Lyapunov dimension for the Chen and Lu systems , 2015, 1504.04726.

[9]  T. N. Mokaev,et al.  Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system , 2015, 1504.04723.

[10]  Sundarapandian Vaidyanathan,et al.  A Memristor-Based Hyperchaotic System with Hidden Attractors: Dynamics, Synchronization and Circuital Emulating , 2015 .

[11]  Huagan Wu,et al.  Complex transient dynamics of hidden attractors in a simple 4D system , 2015 .

[12]  Gennady A. Leonov,et al.  Existence criterion of homoclinic trajectories in the Glukhovsky–Dolzhansky system , 2015 .

[13]  Sergey P. Kuznetsov,et al.  Co-existing hidden attractors in a radio-physical oscillator system , 2015 .

[14]  Bocheng Bao,et al.  Finding hidden attractors in improved memristor-based Chua''s circuit , 2015 .

[15]  Erik Mosekilde,et al.  Multistability and hidden attractors in a multilevel DC/DC converter , 2015, Math. Comput. Simul..

[16]  Zhouchao Wei,et al.  Hidden Attractors and Dynamical Behaviors in an Extended Rikitake System , 2015, Int. J. Bifurc. Chaos.

[17]  Bocheng Bao,et al.  Dynamics of self-excited attractors and hidden attractors in generalized memristor-based Chua’s circuit , 2015 .

[18]  I. M. Burkin,et al.  Analytical-numerical methods of finding hidden oscillations in multidimensional dynamical systems , 2014 .

[19]  Julien Clinton Sprott,et al.  A New Cost Function for Parameter Estimation of Chaotic Systems Using Return Maps as Fingerprints , 2014, Int. J. Bifurc. Chaos.

[20]  Zhouchao Wei,et al.  Hidden Hyperchaotic Attractors in a Modified Lorenz-Stenflo System with Only One Stable Equilibrium , 2014, Int. J. Bifurc. Chaos.

[21]  G. A. Leonov,et al.  Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations , 2014, 1410.2016.

[22]  Nikolay V. Kuznetsov,et al.  On differences and similarities in the analysis of Lorenz, Chen, and Lu systems , 2014, Appl. Math. Comput..

[23]  Awadhesh Prasad,et al.  Existence of Perpetual Points in Nonlinear Dynamical Systems and Its Applications , 2014, Int. J. Bifurc. Chaos.

[24]  Gennady A. Leonov,et al.  Fishing principle for homoclinic and heteroclinic trajectories , 2014 .

[25]  V. Afraimovich,et al.  Scientific heritage of L.P. Shilnikov , 2014 .

[26]  U. Feudel,et al.  Control of multistability , 2014 .

[27]  Yiping Lin,et al.  Hidden Attractors and Dynamics of a General Autonomous van der Pol-Duffing Oscillator , 2014, Int. J. Bifurc. Chaos.

[28]  Luigi Fortuna,et al.  Dynamics and Synchronization of a Novel Hyperchaotic System Without Equilibrium , 2014, Int. J. Bifurc. Chaos.

[29]  Rongrong Wang,et al.  A new finding of the existence of hidden hyperchaotic attractors with no equilibria , 2014, Math. Comput. Simul..

[30]  Irene M. Moroz,et al.  Degenerate Hopf bifurcations, hidden attractors, and control in the extended Sprott E system with only one stable equilibrium , 2014 .

[31]  Sajad Jafari,et al.  Three-dimensional chaotic autonomous system with only one stable equilibrium: Analysis, circuit design, parameter estimation, control, synchronization and its fractional-order form , 2014 .

[32]  Nikolay V. Kuznetsov,et al.  Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor , 2014, Commun. Nonlinear Sci. Numer. Simul..

[33]  Julien Clinton Sprott,et al.  Coexisting Hidden Attractors in a 4-D Simplified Lorenz System , 2014, Int. J. Bifurc. Chaos.

[34]  Nikolay V. Kuznetsov,et al.  Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor , 2014 .

[35]  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.

[36]  Qingdu Li,et al.  On hidden twin attractors and bifurcation in the Chua’s circuit , 2014 .

[37]  Awadhesh Prasad,et al.  Complicated basins and the phenomenon of amplitude death in coupled hidden attractors , 2014 .

[38]  Julien Clinton Sprott,et al.  Chaotic flows with a single nonquadratic term , 2014 .

[39]  Julien Clinton Sprott,et al.  Heat conduction, and the lack thereof, in time-reversible dynamical systems: generalized Nosé-Hoover oscillators with a temperature gradient. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Julien Clinton Sprott,et al.  Simple Chaotic flows with One Stable equilibrium , 2013, Int. J. Bifurc. Chaos.

[41]  Julien Clinton Sprott,et al.  Simple chaotic flows with a line equilibrium , 2013 .

[42]  Michael Eckert,et al.  Arnold Sommerfeld: Science, Life and Turbulent Times 1868-1951 , 2013 .

[43]  Julien Clinton Sprott,et al.  Coexistence of Point, periodic and Strange attractors , 2013, Int. J. Bifurc. Chaos.

[44]  M. Zaks,et al.  Sequences of gluing bifurcations in an analog electronic circuit , 2013, 1304.6760.

[45]  Gennady A. Leonov,et al.  Shilnikov Chaos in Lorenz-like Systems , 2013, Int. J. Bifurc. Chaos.

[46]  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.

[47]  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 .

[48]  Gennady A. Leonov,et al.  General existence conditions of homoclinic trajectories in dissipative systems. Lorenz, Shimizu–Morioka, Lu and Chen systems , 2012 .

[49]  P. Neittaanmaki,et al.  Drilling systems failures and hidden oscillations , 2012, 2012 IEEE 4th International Conference on Nonlinear Science and Complexity (NSC).

[50]  Nikolay V. Kuznetsov,et al.  Hidden attractor in smooth Chua systems , 2012 .

[51]  Guanrong Chen,et al.  Constructing a chaotic system with any number of equilibria , 2012, 1201.5751.

[52]  S. Pilyugin,et al.  Theory of pseudo-orbit shadowing in dynamical systems , 2011 .

[53]  Nikolay V. Kuznetsov,et al.  Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems , 2011 .

[54]  Peter E. Kloeden,et al.  Nonautonomous Dynamical Systems , 2011 .

[55]  Harry Gingold,et al.  On completeness of quadratic systems , 2011 .

[56]  Nikolay V. Kuznetsov,et al.  Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuits , 2011 .

[57]  G. Leonov,et al.  Localization of hidden Chuaʼs attractors , 2011 .

[58]  G. Leonov,et al.  Localization of hidden attractors in smooth Chua's systems , 2011 .

[59]  Gennady A. Leonov,et al.  The dimension formula for the Lorenz attractor , 2011 .

[60]  L. Barreira,et al.  Dimension estimates in smooth dynamics: a survey of recent results , 2010, Ergodic Theory and Dynamical Systems.

[61]  Gennady A. Leonov,et al.  Lyapunov quantities and limit cycles of two-dimensional dynamical systems. Analytical methods and symbolic computation , 2010 .

[62]  Yuan Yan Tang,et al.  On Lorenz-like Dynamic Systems with Strengthened Nonlinearity and New Parameters , 2010, Int. J. Wavelets Multiresolution Inf. Process..

[63]  Luca Dieci,et al.  SVD algorithms to approximate spectra of dynamical systems , 2008, Math. Comput. Simul..

[64]  Nikolay K. Vitanov,et al.  Analytical and numerical investigation of two families of Lorenz-like dynamical systems , 2007 .

[65]  P. Giesl Construction of Global Lyapunov Functions Using Radial Basis Functions , 2007 .

[66]  Nikolay V. Kuznetsov,et al.  Time-Varying Linearization and the Perron Effects , 2007, Int. J. Bifurc. Chaos.

[67]  V. Rasvan,et al.  Three lectures on dissipativeness , 2006, 2006 IEEE International Conference on Automation, Quality and Testing, Robotics.

[68]  G. Leonov,et al.  On stability by the first approximation for discrete systems , 2005, Proceedings. 2005 International Conference Physics and Control, 2005..

[69]  S. Siegmund,et al.  On Dimension and Metric Properties of Trajectory Attractors , 2005 .

[70]  Guanrong Chen,et al.  Hopf bifurcation Control Using Nonlinear Feedback with Polynomial Functions , 2004, Int. J. Bifurc. Chaos.

[71]  Guanrong Chen,et al.  On a Generalized Lorenz Canonical Form of Chaotic Systems , 2002, Int. J. Bifurc. Chaos.

[72]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[73]  Vaithianathan Venkatasubramanian,et al.  Stable operation of a simple power system with no equilibrium points , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[74]  V. Chepyzhov,et al.  Attractors for Equations of Mathematical Physics , 2001 .

[75]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[76]  Brian R. Hunt,et al.  Maximum local Lyapunov dimension bounds the box dimension of chaotic attractors , 1996 .

[77]  Kapitaniak Uncertainty in coupled chaotic systems: Locally intermingled basins of attraction. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[78]  J. Sprott,et al.  Some simple chaotic flows. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[79]  R. Temam Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag , 1993 .

[80]  Igor Chueshov,et al.  Global attractors for non-linear problems of mathematical physics , 1993 .

[81]  Kapitaniak Generating strange nonchaotic trajectories. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[82]  Tomasz Kapitaniak,et al.  Chaotic oscillators : theory and applications , 1992 .

[83]  V. Chepyzhov,et al.  Unbounded attractors of evolution equations , 1992 .

[84]  M. Vishik,et al.  Attractors of Evolution Equations , 1992 .

[85]  O. Ladyzhenskaya,et al.  Attractors for Semigroups and Evolution Equations , 1991 .

[86]  Brian A. Coomes,et al.  The Lorenz system does not have a polynomial flow , 1989 .

[87]  L. Chua,et al.  The double scroll family , 1986 .

[88]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[89]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[90]  S. Nosé A molecular dynamics method for simulations in the canonical ensemble , 1984 .

[91]  B. Aulbach,et al.  Asymptotic stability regions via extensions of Zubov's method—I , 1983 .

[92]  C. Sparrow The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors , 1982 .

[93]  Mathukumalli Vidyasagar,et al.  Maximal lyapunov functions and domains of attraction for autonomous nonlinear systems , 1981, Autom..

[94]  F. Ledrappier,et al.  Some relations between dimension and Lyapounov exponents , 1981 .

[95]  O. Rössler An equation for continuous chaos , 1976 .

[96]  M. Hénon,et al.  A two-dimensional mapping with a strange attractor , 1976 .

[97]  R. Fitts,et al.  Two counterexamples to Aizerman's conjecture , 1966 .

[98]  P. Hartman Ordinary Differential Equations , 1965 .

[99]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[100]  N. Levinson,et al.  Transformation Theory of Non-Linear Differential Equations of the Second Order , 1944 .

[101]  Balth. van der Pol Jun. LXXXVIII. On “relaxation-oscillations” , 1926 .

[102]  Nikolay V. Kuznetsov,et al.  Nonlinear analysis of classical phase-locked loops in signal's phase space , 2014 .

[103]  Nikolay V. Kuznetsov,et al.  Hidden attractors in dynamical systems: systems with no equilibria, multistability and coexisting attractors , 2014 .

[104]  Nikolay V. Kuznetsov,et al.  Analytical-Numerical Localization of Hidden Attractor in Electrical Chua’s Circuit , 2013 .

[105]  Nikolay V. Kuznetsov,et al.  Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation , 2013, NOSTRADAMUS.

[106]  Nikolay V. Kuznetsov,et al.  Hidden oscillations in stabilization system of flexible launcher with saturating actuators , 2013 .

[107]  Nikolay V. Kuznetsov,et al.  Visualization of Four Normal Size Limit Cycles in Two-Dimensional Polynomial Quadratic System , 2013 .

[108]  Nikolay V. Kuznetsov,et al.  Hidden Oscillations in Aircraft Flight Control System with Input Saturation , 2013, PSYCO.

[109]  Gennady A. Leonov,et al.  Lyapunov functions in the attractors dimension theory , 2012 .

[110]  Alexander Lanzon,et al.  A Robust Kalman Conjecture for First-Order Plants , 2012, ROCOND.

[111]  Nikolay V. Kuznetsov,et al.  Analytical-numerical methods for investigation of hidden oscillations in nonlinear control systems , 2011 .

[112]  Nikolay V. Kuznetsov,et al.  Hidden Attractor in Chua's Circuits , 2011, ICINCO.

[113]  Nikolay V. Kuznetsov,et al.  Hidden oscillations in nonlinear control systems , 2011 .

[114]  Nikolay V. Kuznetsov,et al.  Analytical-numerical method for attractor localization of generalized Chua's system , 2010, PSYCO.

[115]  Alexander L. Fradkov,et al.  Slow motions in systems with inertially excited vibrations , 2007, PSYCO.

[116]  G. Leonov Strange attractors and classical stability theory , 2006 .

[117]  A. Babin Chapter 14 - Global Attractors in PDE , 2006 .

[118]  V. Boichenko,et al.  Dimension theory for ordinary differential equations , 2005 .

[119]  Michael Dellnitz,et al.  Chapter 5 - Set Oriented Numerical Methods for Dynamical Systems , 2002 .

[120]  Nikolay V. Kuznetsov,et al.  Counterexample of Perron in the Discrete Case , 2001 .

[121]  S. Evtimov,et al.  On the Lorenz System with Strengthened Nonlinearity , 2000 .

[122]  George Osipenko,et al.  Construction of attractors and filtrations , 1999 .

[123]  David E. Stewart,et al.  A NEW ALGORITHM FOR THE SVD OF A LONG PRODUCT OF MATRICES AND THE STABILITY OF PRODUCTS , 1997 .

[124]  G. Sell Global attractors for the three-dimensional Navier-Stokes equations , 1996 .

[125]  Sergej Celikovský,et al.  Bilinear systems and chaos , 1994, Kybernetika.

[126]  Gennady A. Leonov,et al.  Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors , 1992 .

[127]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[128]  Gary Hosler-Meisters Polynomial flows on $R^n$ , 1989 .

[129]  N. Barabanov,et al.  On the Kalman problem , 1988 .

[130]  G. Leonov,et al.  Attraktorlokalisierung des Lorenz-Systems , 1987 .

[131]  Gennady A. Leonov,et al.  Attraktoreingrenzung für nichtlineare Systeme , 1987 .

[132]  G. Leonov,et al.  Das RÖSSLER‐System ist nicht dissipativ im Sinne von LEVINSON , 1986 .

[133]  J. Yorke,et al.  Chaotic behavior of multidimensional difference equations , 1979 .

[134]  吉沢 太郎 Stability theory by Liapunov's second method , 1966 .

[135]  N. Levinson,et al.  A Second Order Differential Equation with Singular Solutions , 1949 .

[136]  F. Tricomi,et al.  Integrazione di un' equazione differenziale presentatasi in elettrotecnica , 1933 .

[137]  Hamel Georg Duffing, Ingenieur: Erzwungene Schwingungen bei veränderlicher Eigenfrequenz und ihre technische Bedeutung. Sammlung Vieweg. Heft 41/42, Braunschweig 1918. VI+134 S , 1921 .

[138]  L. Rayleigh,et al.  The theory of sound , 1894 .

[139]  Zhouchao Wei,et al.  International Journal of Bifurcation and Chaos C World Scientific Publishing Company Constructing a Novel No–equilibrium Chaotic System , 2022 .