Academic Paper
Tomomichi Nakamura, Tetsushi Ueta, A novel discrete chaotic map with intriguing periodicity and bifurcation structure, World Scientific, International Journal of Bifurcation and Chaos, Vol.34, pp.5-34, June 2025.
Abstract: We introduce a novel chaotic dynamical system formulated as a second-order difference equation.The model includes one time-delay linear term and one nonlinear term composed of the productof two different time delay terms. As a result, the nonlinear term gives rise to strange periods. Thedynamical behaviours of the model are investigated by the Lyapunov spectrum and bifurcationdiagram. We found that the model can have a positive Lyapunov exponent. We also found thatwhile the bifurcation diagram has a typical Arnold tongue structure, there are unique shapesthat show the progression of overlapping sh-hooks in the synchronization region.