On the study of control and anti-control in magnetoconvection

Abstract Instability and the onset of chaos is analyzed in the phenomenon of magnetoconvection with the help of phase space analysis, Lyapunov exponents and temporal variation of predictability. In contrast to the previous analysis in the literature, we have explored the period doubling route to chaos, which is shown to be equally effective as Hopf bifurcation. Initially the physical system of magnetoconvection with positive Chandrasekhar number is analyzed and next a prototype of a new dynamical system given for q

[1]  F. Christiansen,et al.  Computing Lyapunov spectra with continuous Gram - Schmidt orthonormalization , 1996, chao-dyn/9611014.

[2]  Alastair M. Rucklidge,et al.  Chaos in magnetoconvection , 1994 .

[3]  Tom T. Hartley,et al.  Adaptive estimation and synchronization of chaotic systems , 1991 .

[4]  W. Ditto,et al.  Controlling chaos in the brain , 1994, Nature.

[5]  Response to ‘‘Comment on ‘Bifurcations from periodic solution in a simplified model of two‐dimensional magnetoconvection’ ’’ [Phys. Plasmas 2, 2945 (1995)] , 1996 .

[6]  Saddle-node bifurcation without a reinjection process in the temporal intermittency , 1998 .

[7]  V. Arnold Mathematical Methods of Classical Mechanics , 1974 .

[8]  N. Bekki,et al.  Bifurcations from periodic solution in a simplified model of two‐dimensional magnetoconvection , 1995 .

[9]  E. Knobloch,et al.  Oscillatory and steady convection in a magnetic field , 1981, Journal of Fluid Mechanics.

[10]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

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

[12]  Zhihong Lin,et al.  Gyrokinetic particle simulation of neoclassical transport , 1995 .

[13]  S. Chandrasekhar Hydrodynamic and Hydromagnetic Stability , 1961 .

[14]  S. Chandrasekhar CXXXI. On the inhibition of convection by a magnetic field : II , 1952 .

[15]  P. Grassberger,et al.  Dimensions and entropies of strange attractors from a fluctuating dynamics approach , 1984 .

[16]  Edgar Knobloch,et al.  Bifurcations in a model of magnetoconvection , 1983 .

[17]  N. Bekki,et al.  Devil's Staircase in a Dissipative Fifth-Order System , 2000 .

[18]  M. Bernardo An adaptive approach to the control and synchronization of continuous-time chaotic systems , 1996 .

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

[20]  Jon M. Nese Quantifying local predictability in phase space , 1989 .

[21]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[22]  Edgar Knobloch,et al.  Oscillations in double-diffusive convection , 1981, Journal of Fluid Mechanics.

[23]  William H. Press,et al.  Numerical recipes in C , 2002 .

[24]  Mogens H. Jensen,et al.  Global universality at the onset of chaos: Results of a forced Rayleigh-Benard experiment. , 1985 .

[25]  Ott,et al.  Preserving chaos: Control strategies to preserve complex dynamics with potential relevance to biological disorders. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Edgar Knobloch,et al.  Nonlinear periodic convection in double-diffusive systems , 1981 .

[27]  E. Knobloch,et al.  Comment on ‘‘Bifurcations from periodic solution in a simplified model of two‐dimensional magnetoconvection,’’ by N. Bekki and T. Karakisawa [Phys. Plasmas 2, 2945 (1995)] , 1996 .

[28]  Schwartz,et al.  Tracking sustained chaos: A segmentation method , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  George Veronis,et al.  Motions at subcritical values of the Rayleigh number in a rotating fluid , 1966, Journal of Fluid Mechanics.

[30]  G. Benettin,et al.  Kolmogorov Entropy and Numerical Experiments , 1976 .

[31]  N. Bekki Torus Knot in a Dissipative Fifth-Order System , 2000 .