Nonlinear dynamics and chaos

S. H. Strogatz, Nonlinear Dynamics and Chaos With Applications to Phy.dcs, Biology, CJiemistry and Engineering Addison Wesley, Reading (1994). 

WIGGINS, S. Introduction to Applied Nonlinear Dynamics and Chaos. Springer-Verlag, New York, Berlin, 1989... 

Strogatz, S. H. (1994). NonLinear Dynamics and Chaos, With Applications to Physics, Biology, Chemistry, and Engineering. Perseus Book Group. 

Steward, H. Bruce Thompson, J. M. Nonlinear Dynamics and Chaos Wiley Chichester, 1986. 

Strogatz, S.H. Nonlinear Dynamics and Chaos, with Applications to Physics, Biology, Chemistry and Engineering, Addison-Wesley Publishing Company Reading, MA, 1994. 

J. M. T. Thompson and H. B. Stewart Nonlinear dynamics and chaos. Wiley and Sons, Chichester, 1986. 

Numerous applications of nonlinear dynamics and chaos theory to cardiac physiology have been published [581]. Many techniques, either statistical, like spec-... 

Nonlinear analysis requires the use of new techniques such as embedding of data, calculating correlation dimensions, Lyapunov exponents, eigenvalues of singular-valued matrices, and drawing trajectories in phase space. There are many excellent reviews and books that introduce the subject matter of nonlinear dynamics and chaos [515,596-599]. 

Dokoumetzidis, A., Iliadis, A., and Macheras, P., Nonlinear dynamics and chaos theory Concepts and applications relevant to pharmacodynamics, Pharmaceutical Research, Vol. 18, No. 4, 2001, pp. 415-426. 

Thompson JMT, Stewart HB (1986) Nonlinear dynamics and chaos. John Wiley and sons... 

McCauley, J.L. (1988). An introduction to nonlinear dynamics and chaos theory, Physica Scripta T20, 5-57. 

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. 

Nonlinear dynamics and chaos with applications to physics, biology, chemistry, and engineering / Steven H. Strogatz. 

Strogatz S (1996) Nonlinear dynamics and chaos, chap 7.6. Addison-Wesley... 

Collins and Schranz have studied resonance phenomena in models of torsional isomerization. A number of useful reviews on progress in the use of nonlinear dynamics and chaos theory to describe molecular phenomena are avail-... 

N. B. Tufillaro, T. Abbott, and J. Reilly, An Experimental Approach to Nonlinear Dynamics and Chaos, Addison-Wesley, Redwood City, CA, 1992. 

Chaotic behavior in nonlinear dissipative systems is characterized by the existence of a new type of attractor, the strange attractor. The name comes from the unusual dimensionality assigned to it. A steady state attractor is a point in phase space, whereas a limit cycle attractor is a closed curve. The steady state attractor, thus, has a dimension of zero in phase space, whereas the limit cycle has a dimension of one. A torus is an example of a two-dimensional attractor because trajectories attracted to it wind around over its two-dimensional surface. A strange attractor is not easily characterized in terms of an integer dimension but is, perhaps surprisingly, best described in terms of a fractional dimension. The strange attractor is, in fart, a fractal object in phase space. The science of fractal objects is, as we will see, intimately connected to that of nonlinear dynamics and chaos. 

Strogatz, S. H. 1994. Nonlinear Dynamics and Chaos. Addison-Wesley Reading, Mass. Strunina, A. G. Dvoryankin, A. V. Merzhanov, A. G. 1983. Unstable Regimes of Thermite System Combustion, Combust. Explos. Shock Waves 19, 158-163. 

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