Abstract
In this study, some important physical systems, which are examples of dynamic systems that exhibit chaotic behavior, are given. These are field models with spinor fields, which are especially important in particle physics. In this study, Duffing, Thirring and Dirac-Gursey systems will be discussed. The Duffing equation is a famous nonlinear differential equation that exemplifies a dynamical system that exhibits chaotic behavior. Various forms of the Duffing equation are used to describe many nonlinear systems. The Duffing equation serves as a test model for us to understand the dynamics of the nonlinear spinor field models we are working on. Thirring system is a relativistic field theory for the interaction of fermions. It is two-dimensional massless system. Since the Thirring system is the simplest nonlinear spinor system, it has an important place in particle physics as a toy model. The Dirac-Gursey system was proposed in 1956 to realize the dream of Heisenberg and his friends. It is the first nonlinear spinor wave equation with four dimensions and conformal invariance. Due to these properties, it has a wider symmetry than the Dirac equation and the equations proposed by Heisenberg et al. Gursey became the first physicist to test conformal invariance in spinor field theories with this system he proposed in 1956.
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