One useful book is

Braun, Oleg M., and Yuri S. Kivshar. The Frenkel-Kontorova model: concepts, methods, and applications. Springer Science & Business Media, 2013.

The book about the chaotic (nonlinear) systems of the reputable author:

Sprott, Julien Clinton, and Julien C. Sprott. Chaos and time-series analysis. Vol. 69. Oxford: Oxford University Press, 2003.

I would recommend the following two books which are really good for beginners.

1.) Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering by Steven H. Strogatz

2.) Nonlinear Dynamics and Chaos by Thompson and Stewart

Thank you very much for your nice cooperation.

here is a very straightforward and concise option:

-> stephen lynch, dynamical systems with python/mathematica/maple/matlab

Steven H. Strogatz

Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering

I think this book is the best.

Nonlinear Systems, P.G. Drazin, Cambridge Texts in Applied Mathematics,

ISBN 0-521-40668-4

Dear Schlegel

Thaonk you very much for your nice cooperation.

Ali H. Nayfeh, Dean T. Mook, Nonlinear Oscillations, 1979 (first edition), 2004 (another edition), Willey - VCH.

Dear Dumitru Deleanu

Thank you very much for your nice suggestion

Besides the abovementioned books and references these older and already classical books by Minorsky (Nonlinear oscillations) and Andronov & Chaikin (Theory of oscillations) may be of interest, as well as the two volumes by Attle-Jackson, Perspectives of nonlinear dynamics.

Dear Suárez-Ántola

Thank you very much for your nice cooperation.

Is the book "nonlinear dynamics by Attle-Jackson" the new version of the classical books by Minorsky (Nonlinear oscillations) and Andronov & Chaikin (Theory of oscillations)?

Actullay, I am looking for the new version of the book of "Nonlinear Oscillations by Ali H. Nayfeh, Dean T. Mook", "Nonlinear oscillations by Mickens" etc.

Alal

Dear Dr. Alal Hosen:

The two volume book of Attle-Jackson has a wider content than the non-linear oscillation books of Minorsky and Andronov and Chaikin, but less details in certain topics specific of nonlinear oscillations.

The nonlinear methods used to construct nonlinear models to describe the dynamics of physical, chemical and biological systems, as well as several related topics of pure mathematics, are developed in "Perspectives of nonlinear dynamics" thinking in the applied scientists. An example of the abovementioned topics of pure mathematics, that is not always well known by applied scientists, is Reubel´s theorem about low order universal differential equations and the implications of Reubel´s theorem for mathematical modeling.

My answer to your question: ("Can anyone suggest me, which book is the most helpful for mathematical modeling of the nonlinear oscillatory problems in dynamical systems?") was oriented to add some books that complement the very good suggestions that appear in the answers of other people.

Perhaps you can give us some additional details so that we can suggest, if it is within our means, some more specific bibliography.

Dear Dr. Alal Hosen:

When you make reference to "Nonlinear oscillations by Mickens" , do you mean "Truly Nonlinear Oscillatios: Harmonic Balance, Parameter Expansions, Iteration, and Averaging Methods", "Oscillations in planar dynamic systems" or both books?

Dear Suárez-Ántola

Thanks for you suggestion.

These books already I have you mentioned. My searching books are the latest version related to that by other several authors.

To be best of my knowledge, some good books that may related to your interests:

• Nonlinear Dynamics and Chaos - with Applications to Physics, Biology, Chemistry, and Engineering: Steven Strogatz (1994).
• Elements of Applied Bifurcation Theory: Yuri A. Kuznetsov.
• Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields: John Guckenheimer, , P. J. Holmes.
• Introduction to Applied Nonlinear Dynamical Systems and Chaos: Stephen Wiggins.
• Dynamical Systems: Stability, Symbolic Dynamics, and Chaos: Clark Robinson (1995).

I can add

- Nonlinear oscillations, N. Minorsky

- Lecture notes on nonlinear vibrations, Richard Rand (free online)

Dear Erik

Thanks for your suggestion