CHAOTIC DYNAMICS AND BIFURCATION ANALYSIS OF NE12 SYSTEM - Ismail Yunus, Muhammad
Using custom software, Julien Clinton Sprott with Sajad Jafari and M. R. H. Golpayegani, found 17 new systems of nonlinear ordinary differential equations, that published at 2013, shown to have chaotic dynamics with the simplest form, in the sense algebraic simplicity (nonlinear function in the form of quadratic polynomials), and also not having any equilibrium points for a specific value of parameter. In this thesis, one of the system named NE12 will be studied to found out how the system behave and how chaotic solution surfaced. Using analytical and numerical tool, it will be shown that NE12 will have fold and Hopf supercritical bifurcations. In NE12 case, its periodic solutions will shown to have cascade of period-doubling bifurcation. Another result that will be numerically shown in this thesis is the creation of homoclinic orbits that later will be destroyed by varying the parameter. Chaotic dynamics of the system will be quantify by using limit-set diagram, Lyapunov exponent, and also Kaplan-Yorke dimension of the system.