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Ali Hasan Nayfeh (Arabic: علي نايفة) (21 December 1933 – 27 March 2017) [1] was a Palestinian-Jordanian mathematician, mechanical engineer and physicist. [2] He is regarded as the most influential scholar and scientist in the area of applied nonlinear dynamics in mechanics and engineering. [3]
Nonlinear Dynamics. Models of bifurcation and chaos by Elmer G. Wiens; Sci.Nonlinear FAQ 2.0 (Sept 2003) provides definitions, explanations and resources related to nonlinear science; Online books or lecture notes. Geometrical theory of dynamical systems. Nils Berglund's lecture notes for a course at ETH at the advanced undergraduate level.
He is considered one of the founders of nonlinear dynamics and chaos theory. His work on turbulence contributed to an understanding of the transition from laminar to turbulent flow. He provided contributions to the description of a laser using nonlinear dynamics. With Stefan Thomae he produced a value for the Feigenbaum constant. [1]
Muthusamy Lakshmanan was born on 25 March 1946 in Pollachi, in the Coimbatore district of the south Indian state of Tamil Nadu.He graduated in science from NGM College in Pollachi in 1966 and earned his master's degree in physics (MSc) at Madras Christian College of the University of Madras in 1969. [2]
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
In practice, unstable dynamics may have deleterious effects on the system (e.g., it may be dangerous for internal states of the system to grow unbounded). These unobservable states may be controllable or at least stable, and so measures can be taken to ensure these states do not cause problems in practice.
As suggested in Lorenz's book entitled The Essence of Chaos, published in 1993, [6]: 8 "sensitive dependence can serve as an acceptable definition of chaos". In the same book, Lorenz defined the butterfly effect as: "The phenomenon that a small alteration in the state of a dynamical system will cause subsequent states to differ greatly from the ...
Balachandran's research spans the fields of applied mathematics, applied physics, mechanics, dynamics, control, and system identification, with an emphasis on the analysis and application of nonlinear phenomena and nonlinear dynamics in diverse systems ranging from rotating machinery, vehicle systems, and space structures to disease dynamics.