Academic Paper
Michiru Katayama, Tetsushi Ueta, Reversal-Time Dynamics of two-dimensional non-autonomous systems, Institute of Electronics, Information and Communication Engineers, Nonlinear Theory and Its Applications, IEICE, Vol.E15-N, No.1, pp.(inpress), Jan. 2025.
Abstract: This study, we discusses the topological type of nonautonomous systems with periodicsolutions when the time variable t increases negatively. When linear approximation holds neara fixed point of the Poincaré map, we confirm that the bifurcation points where the fixed pointbecomes nonhyperbolic are invariant regardless of the time direction however, the stability ofthe fixed point is changed. Consequently, we show that two-dimensional bifurcation diagramsobtained by the brute-force method give different results for positive and reversal-time variablesystems; however, the bifurcation curves are identical. The inverted time variable system is usefulfor visualizing the completely unstable fixed point, because the repeller can be observed as anattractor. Furthermore, in certain models, chaotic attractors with a wide parameter range existin reversal time variable systems.