Bifurcation Dynamics in Polynomial Discrete Systems

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Focusing on bifurcation dynamics in 1-dimensional polynomial nonlinear discrete systems, this book explores mathematical conditions for bifurcations, including simple and higher-order singularity period-1 fixed points. It delves into bifurcation trees leading from period-1 to chaos through period-doubling and saddle-node bifurcations. Additionally, it introduces methods for period-2 and period-doubling renormalization, and reveals the mechanisms behind the period-doublization of period-n fixed points, providing valuable insights into contemporary research in the field.