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## NONLINEAR OSCILLATIONS OF VECTOR FIELDS WITH APPLICATIONS IN PHYSICS

### Tahmineh Azizi

#### Kansas State University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakb7d26dab0a376382436ffe78af49d435').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyb7d26dab0a376382436ffe78af49d435 = 't&#97;z&#105;z&#105;' + '&#64;'; addyb7d26dab0a376382436ffe78af49d435 = addyb7d26dab0a376382436ffe78af49d435 + 'ks&#117;' + '&#46;' + '&#101;d&#117;'; var addy_textb7d26dab0a376382436ffe78af49d435 = 't&#97;z&#105;z&#105;' + '&#64;' + 'ks&#117;' + '&#46;' + '&#101;d&#117;';document.getElementById('cloakb7d26dab0a376382436ffe78af49d435').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyb7d26dab0a376382436ffe78af49d435 + '\'>'+addy_textb7d26dab0a376382436ffe78af49d435+'<\/a>';

A dynamical system describes the evolution of a system over time using a set of mathematical laws. Also, it can be used to predict the interactions between different components of a system. There are two main methods to model the dynamical behaviors of a system, continuous time modeling, discrete-time modeling. When the time between two measurements is negligible, the continuous time modeling governs the evolution of the system, however, when there is a gap between two measurements, discrete-time system modeling comes to play. Ordinary differential equations are the tool to model a continuous system and iterated maps represent the discrete generations. Investigating local dynamics of equilibrium points of nonlinear systems plays an important role in studying the behavior of dynamical systems. There are many different definitions for stable and unstable solutions in the literature. The main goal to develop stability definitions is exploring the responses or output of a system to perturbation as time approaches infinity. Due to the wide range of application of local dynamical system theory in physics, biology, economics and social science, it still attracts many researchers to play with its definitions to find out the answers for their questions. In this study, we look at local dynamical behavior of famous dynamical systems, Hénon-Heiles system, Duffing oscillator and Van der Pol equation and analyze them.