A new deterministic model for chaotic reversals

Abstract We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced by crisis-induced intermittency, following a mechanism different from what is generally observed in similar deterministic models. Despite its simplicity, this system therefore generates a rich dynamics, able to model more complex physical systems. In particular, a comparison with reversals of the magnetic field of the Earth shows a surprisingly good agreement, and highlights the relevance of deterministic chaos to describe geomagnetic field dynamics.

[1]  B. Dubrulle,et al.  Magnetic field reversals in an experimental turbulent dynamo , 2007, physics/0701076.

[2]  Grebogi,et al.  Critical exponents for crisis-induced intermittency. , 1987, Physical review. A, General physics.

[3]  Masaru Kono,et al.  Rikitake two‐disk dynamo and paleomagnetism , 1987 .

[4]  R Volk,et al.  Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium. , 2007, Physical review letters.

[5]  P. Olson,et al.  Mantle plumes link magnetic superchrons to phanerozoic mass depletion events , 2007 .

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

[7]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[8]  L. Meynadier,et al.  Geomagnetic dipole strength and reversal rate over the past two million years , 2005, Nature.

[9]  P. Nozières.  Reversals of the earth's magnetic field: An attempt at a relaxation model , 1978 .

[10]  S. Cande,et al.  Revised calibration of the geomagnetic polarity timescale for the Late Cretaceous and Cenozoic , 1995 .

[11]  S. Wiggins.  Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

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

[13]  M. Proctor,et al.  A Heteroclinic model of geodynamo reversals and excursions , 2001 .

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

[15]  Paul H. Roberts,et al.  The role of the Earth's mantle in controlling the frequency of geomagnetic reversals , 1999, Nature.

[16]  Emmanuel Dormy,et al.  Simple mechanism for reversals of earth's magnetic field. , 2008, Physical review letters.

[17]  D. Schmitt,et al.  The geodynamo as a bistable oscillator , 2001 .

[18]  J. Yorke,et al.  CHAOTIC ATTRACTORS IN CRISIS , 1982 .

[19]  M. McElhinny,et al.  Reversals of the Earth's magnetic field and temporal variations of the dynamo families , 1991 .

[20]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .

[21]  A low-order model of the shear instability of convection: chaos and the effect of noise , 1990 .

[22]  Emmanuel Dormy,et al.  Morphology of field reversals in turbulent dynamos , 2010 .

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

[24]  G. Glatzmaier,et al.  A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle , 1995 .

[25]  P Harabaglia,et al.  Clustering of polarity reversals of the geomagnetic field. , 2006, Physical review letters.

[26]  S. Fauve,et al.  Chaotic dynamics of the magnetic field generated by dynamo action in a turbulent flow , 2008 .