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范德珀尔振子及受迫范德珀尔振子呈现的分岔性质，为最初被人类观测到的混沌现象之一，叩开了混沌世界的大门。1945年英国数学家卡特赖特（M.Cartwright）和李特伍德（J.Littlewood）在对受迫范德珀尔振子的研究中，在理论层面首次证明受迫范德珀尔方程存在[[奇异解]]，预示了混沌的可能性<ref name="Cartwright_Littlewood_On_non-linear_differential_equations_of_the_second_order" />。随后，日本学者上田睆亮（Ueda Yoshisuke）于1961年首次在[[模拟计算机]]上观察到混沌[[吸引子]]<ref name="Hayashi_Shibayama_Ueda_Quasi-periodic_Oscillations_in_Self-oscillatory_Systems_with_External_Force" />，随着后续研究的深入，混沌理论的面纱也逐渐被科学家们所揭晓。

范德珀尔振子及受迫范德珀尔振子呈现的分岔性质，为最初被人类观测到的混沌现象之一，叩开了混沌世界的大门。1945年英国数学家卡特赖特（M.Cartwright）和李特伍德（J.Littlewood）在对受迫范德珀尔振子的研究中，在理论层面首次证明受迫范德珀尔方程存在[[奇异解]]，预示了混沌的可能性<ref name="Cartwright_Littlewood_On_non-linear_differential_equations_of_the_second_order" />。随后，日本学者上田睆亮（Ueda Yoshisuke）于1961年首次在[[模拟计算机]]上观察到混沌[[吸引子]]<ref name="Hayashi_Shibayama_Ueda_Quasi-periodic_Oscillations_in_Self-oscillatory_Systems_with_External_Force" />，随着后续研究的深入，混沌理论的面纱也逐渐被科学家们所揭晓。

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