Space time evolution of dynamical systems with few degrees of freedom

The thesis work involves analysis of chaotic behavior in physical systems modelled by low dimensional equation of motion. The paradigm of chaos became prominent in the late 1960's. This has stimulated interest in this field, causing a rapid rise in the quality and quantity of research. As one example of analysing chaotic behavior from a Lagrangian dynamical system, the Yang-Mills-Higgs system is studied which exhibits local instability but possesses a globally ordered phase by spantaneous symmetry breaking. Chaotic behavior and chaos to order transitions are analyzed. Addition of oscillatory term the region where the chaos-order transition occurs identified with an eye on transition back to order. As a second example, regions of chaotic behavior in the parameter space of the Maxwell-Bloch equations (also Lorenz-Haken equations) has been studied as a constrained system. The main part of this work involves identification of chaos in a set of experimental data, the monthly average discharge data of Sakarya River directly. Basic characteristics of chaos such as the irregularity of motion, unpredictability and sensitivity to intial conditions can thus be understood using nonlinear time series methods.. Using this data, possible low dimensional chaotic behavior of Sakarya river flow is investigated. To reveal the chaotic dynamics, maximal positive Lyapunov exponent is calculated from the reconstructed phase space obtained using the phase space reconstruction method. The approach reconstructs a locally equivalent phase space from the scalar time series from which the real system's invariants can be estimated. Positive values for the maximal Lyapunov exponents have been calculated and this is an accepted indicator for chaotic behavior possibility. Analysed data contains the montly average flow rates of eleven main branches of Sakarya river through the years 1960-2000.