Network science An English introductory course for undergraduate students Lecturer: Dr. Cong LI ee@ Fudan University Adaptive Networks and Control Lab
Network Science Lecturer: Dr. Cong LI EE @ Fudan University —— An English introductory course for undergraduate students Adaptive Networks and Control Lab
Synchronization All together now Synchronization Synchronization is one A Universal Concept in Nonlinear Scences of the most pervasive Arkady Pakowvsy, Micluel Rosenblum and Jurgen Kurths phenomena in the Universe
Synchronization: All together now Synchronization is one of the most pervasive phenomena in the Universe
Synchronization story starts from ·克里斯蒂安·惠更斯( Christiaan Huygens,1629年04月 14日-1695年07月08日) ·荷兰物理学家、天文学家、数学家、他是介于伽利略与 牛顿之间一位重要的物理学先驱,是历史上最著名的物 理学家之一,他对力学的发展和光学的研究都有杰出的 贡献,在数学和天文学方面也有卓越的成就,是近代自 然科学的一位重要开拓者。他建立向心力定律,提出动 量守恒原理,改进了计时器
Synchronization story starts from… • 克里斯蒂安·惠更斯(Christiaan Huygens，1629年04月 14日—1695年07月08日) • 荷兰物理学家、天文学家、数学家、他是介于伽利略与 牛顿之间一位重要的物理学先驱,是历史上最著名的物 理学家之一，他对力学的发展和光学的研究都有杰出的 贡献，在数学和天文学方面也有卓越的成就，是近代自 然科学的一位重要开拓者。他建立向心力定律，提出动 量守恒原理，改进了计时器
C. Huygens in 1665 He was ill and in-bed watching the motions of two pendulum clocks he had built To his surprise he detected an odd kind of sympathy between the clocks: regardless of their initial state, the two pendulums soon adopted the same rhythm, one moving left as the other swung right
C. Huygens in 1665 • He was ill and in-bed, watching the motions of two pendulum clocks he had built. • To his surprise, he detected an “odd kind of sympathy” between the clocks: regardless of their initial state, the two pendulums soon adopted the same rhythm, one moving left as the other swung right
From two to more: revisit it! You can also repeat this experiment!
From two to more: Revisit it! • You can also repeat this experiment!
Synchronization of clocks Later, Huygens announced his finding at a special session of the royal Society of London attributing this synchrony to tiny forces transmitted between the clocks by the wooden beam from which they were suspended In 1960s, Arthur Winfree, a (world-leading) theoretical biologist began to study coupled oscillators
Synchronization of Clocks • Later, Huygens announced his finding at a special session of the Royal Society of London, attributing this synchrony to tiny forces transmitted between the clocks by the wooden beam from which they were suspended. • In 1960s, Arthur Winfree, a (world-leading) theoretical biologist began to study coupled oscillators
A, Winfree's observations Arthur Winfree(1942-2002) The blinking of fireflies is one behavior that Winfree studied. As night falls on the jungles of Southeast Asia, fireflies begin to flicker, each following its own rhythm. But over the next hour or so, pockets of synchrony emerge and grow. Thousands of fireflies clustered around individual trees eventually flash as one, switching on and off every second or two to create a stunning entomological light show
A. Winfree’s observations • Arthur Winfree (1942-2002) • The blinking of fireflies is one behavior that Winfree studied. As night falls on the jungles of Southeast Asia, fireflies begin to flicker, each following its own rhythm. But over the next hour or so, pockets of synchrony emerge and grow. Thousands of fireflies clustered around individual trees eventually flash as one, switching on and off every second or two to create a stunning entomological light show
Sciences behind the Romantics
Sciences behind the Romantics……
Fireflies Synchronize their Flashes How does such synchrony come abd firefly has its own cycle of flashes reset when the fly sees a flash from flies become synchronized in this w gradually spreads until large groups oScIllating units communicate by ex prompt other units to alter their tim occurs if these coupling signals are overcome the initial variation in ind Below a threshold, anarchy prevail collective rhythm, ---Winfree
Fireflies Synchronize their Flashes • How does such synchrony come about? In this case, each firefly has its own cycle of flashes, but that rhythm can be reset when the fly sees a flash from a neighbour. Pairs of flies become synchronized in this way, and the effect gradually spreads until large groups are linked. In general, oscillating units communicate by exchanging signals that prompt other units to alter their timing. Synchronization occurs if these ‘coupling’ signals are influential enough to overcome the initial variation in individual frequencies. • “Below a threshold, anarchy prevails; above it, there is a collective rhythm,”--- Winfree
Synchronization is one of the most pervasive phenomena in the Universe More examples here!
Synchronization is one of the most pervasive phenomena in the Universe. More examples here!