Nonlinear science

Molecule and Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science (RIES), Hokkaido University, Sapporo 060-0812 Japan... 

Center for Nonlinear Science, Georgia Institute of Technology, Atlanta, Georgia... 

Damgov, V. N. Nonlinear and Parametric Phenomena Theory and Applications in Radiophysical and Mechanical Systems. Monograph. Series A Monographs (Series of Nonlinear Sciences), Series Editor prof.Leon O. Chua, University of California, Berkeley, World Scientific New Jersey, London, Singapore 2004, 570 p., Chapter 10... 

L.P. Shilnikov, A.L. Shilnikov, P.V. Turaev, and O.L. Chua. Part II. World Scientific, chapter Methods of qualitative theory in nonhnear dynamics. Series in Nonlinear Science, 2001. 

In order to analyze both systems, some techniques from nonlinear science are burrowed. Firstly, a phase portrait is constructed from delay coordinates, a Poincare map is also computed, FFT is exploited to derive a Power Spectrum Density (PSD) Maximum Lyapunov Exponents (MLE) are also calculated from time series. Although we cannot claim chaos, the evidence in this chapter shows the possible chaotic behavior but, mostly important, it exhibits that the oscillatory behavior is intrinsically linked to the controlled systems. The procedures are briefly described before discuss each study case. 

The maximum Lyapunov exponent (MLE) was computed to provide major evidence of nonperiodic oscillatory behavior. MLE is one of the most important features in nonlinear science to distinguish chaotic from non chaotic behavior. Essentially MLE measures the distance between attractor orbits... 

A characteristic feature of nonlinear science generally, and of nonlinear optics in particular, is the common necessity of having to make simplifications, and then approximations in order to solve the equations of even the simplified models. These considerations apply a fortiori to the study of fluctuation phenomena in nonlinear systems, and thus account for the increasing role being played by analog and digital simulations, which enable the behaviour of the model systems to be investigated in considerable detail. 

Zaldivar, J.-M., Bosch, J., Strozzi, F. and Zbilut, J.P. (2005) Early warning detection of runaway initiation using non-linear approaches. Communications in Nonlinear Science and Numerical Simulation, 10 (3), 299. 

A. Pikovsky, M. Rosenblum, and J. Kurths Synchronization - a universal concept in nonlinear sciences. Cambridge University Press, Cambridge, 2001. 

Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe, 657-8501, Japan... 

Campbell, D.K. (1987). Nonlinear science, from paradigms to practicalities, in Los Alamos Science, Vol. 15, ed. N.G. Cooper (Los Alamos Laboratory, Los Alamos). 

The dynamics of systems with many degrees of freedom is an interesting and important subject in various fields of research and ordinary life, ranging from the dynamics of molecules to satellite orbiting. Progress in nonlinear science and dynamical systems has revealed the intricate dynamics occurring in noninteg-rable systems. 

P. Meakin, Fractals, Scaling and Growth Far from Equilibrium, Cambridge Nonlinear Science Series 5, Cambridge University Press, Cambridge, 1998. 

V. Zykov. Simulation of wave processes in excitable media. Transl. from the Russian by Potrans, edited by A. T. Winfree. Nonlinear Science Theory and Applications. Manchester etc. Manchester University Press, 235 p., 1987. 

A. Bayliss, B.J. Matkowsky, A.P. Aldushin, Solid Flame Waves, Chapter 4 in Perspectives and Problems in Nonlinear Science A Celebratory Volume in Honor of Larry Sirovich, Eds. E. Kaplan, J. Marsden. K. Sreenivasan, Springer Verlag, 2003... 

Institute for Nonlinear Science, University of California, San Diego,... 

Dr. Lev S. Tsimring, Institute for Nonlinear Science, University of Cahfomia, San Diego, La Jolla, CA 92093-0402, USA... 

In short, recent experiments are observing phenomena that are far from equilibrium. Therefore, the bases of reaction theory has to be sought in their dynamical origin, which is the basic aim in interdisciplinary research between nonlinear science and chemical reactions. 

K. Showalter, Nonlinear Science Today, 4,1 (1995). Quadratic and Cubic Reaction-Diffusion... 

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