A Rikitake Type System with quadratic Control

A Rikitake type system with quadratic control having a negative tuning parameter is considered and some of the geometrical and dynamical properties are analyzed.

[1]  Guanrong Chen,et al.  From Chaos to Order - Perspectives and Methodologies in Controlling Chaotic Nonlinear Dynamical Systems , 1993 .

[2]  Anania Aron,et al.  On a Hamiltonian Version of the Rikitake System , 2009, SIAM J. Appl. Dyn. Syst..

[3]  T. Bînzar,et al.  A Rikitake type system with one control , 2013 .

[4]  W B Steeb,et al.  Continuous symmetries of the Lorenz model and the Rikitake two-disc dynamo system , 1982 .

[5]  P. Lax INTEGRALS OF NONLINEAR EQUATIONS OF EVOLUTION AND SOLITARY WAVES. , 1968 .

[6]  Li Xian-feng Chaos and Chaos Control of the Rikitake Two-Disk Dynamo , 2006 .

[7]  Alan Weinstein,et al.  Normal modes for nonlinear hamiltonian systems , 1973 .

[8]  H. Whitney Tangents to an Analytic Variety , 1965 .

[9]  W. Steeb,et al.  The Rikitake Two-Disk Dynamo System and Domains with Periodic Orbits , 1999 .

[10]  T. Yajima,et al.  KCC-theory and geometry of the Rikitake system , 2007 .

[11]  A. E. Cook Two disc dynamos with viscous friction and time delay , 1972 .

[12]  C. Valls Rikitake system: analytic and Darbouxian integrals , 2005, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[13]  Jaume Llibre,et al.  Invariant algebraic surfaces of the Rikitake system , 2000 .

[14]  M. Pflaum Analytic and geometric study of stratified spaces , 2001 .

[15]  Keisuke Ito,et al.  Chaos in the Rikitake two-disc dynamo system , 1980 .

[16]  M. Puta Hamiltonian Mechanical Systems and Geometric Quantization , 1993 .

[17]  Richard Cushman,et al.  Global Aspects of Classical Integrable Systems , 2004 .

[18]  Jerrold E. Marsden,et al.  Nonlinear stability of fluid and plasma equilibria , 1985 .

[19]  T. Rikitake,et al.  Oscillations of a system of disk dynamos , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.

[20]  Periodic orbits in the case of a zero eigenvalue , 2007, 0705.2361.

[21]  Philippe Marty,et al.  Chaotic behaviour of the Rikitake dynamo with symmetric mechanical friction and azimuthal currents , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[22]  Jürgen Moser,et al.  Periodic orbits near an equilibrium and a theorem by Alan Weinstein , 1976 .

[23]  R. Hide Structural instability of the Rikitake disk dynamo , 1995 .

[24]  M. Barge Invariant Manifolds and the Onset of Reversal in the Rikitake Two-Disk Dynamo , 1984 .

[25]  A. M. Li︠a︡punov Problème général de la stabilité du mouvement , 1949 .

[26]  Lee Sun-Jin From Chaos to Order , 2011 .

[27]  T. M. Rocha Filho,et al.  Algebraic structures and invariant manifolds of differential systems , 1998 .