Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state. A metaphor for this behavior is that a butterfly flapping its wings in Texas can cause a tornado in Brazil.
In mathematics, specifically bifurcation theory, the Feigenbaum constants are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map. They are named after the physicist Mitchell J. Feigenbaum.
In the study of dynamical systems, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence of observations of the state of that system. The reconstruction preserves the properties of the dynamical system that do not change under smooth coordinate changes, but it does not preserve the geometric shape of structures in phase space.
Steven Henry Strogatz, born August 13, 1959, is an American mathematician and the Susan and Barton Winokur Distinguished Professor for the Public Understanding of Science and Mathematics at Cornell University. He is known for his work on nonlinear systems, including contributions to the study of synchronization in dynamical systems, and for his research in a variety of areas of applied mathematics, including mathematical biology and complex network theory.
Henry Emil Kandrup was an American astrophysicist and professor at the University of Florida, Gainesville. His major contributions were in the areas of galaxy dynamics and plasma physics.
Junuthula N. Reddy is a Distinguished Professor, Regent's Professor, and inaugural holder of the Oscar S. Wyatt Endowed Chair in Mechanical Engineering at Texas A&M University, College Station, Texas, USA.[1] He is an authoritative figure in the broad area of mechanics and one of the researchers responsible for the development of the Finite Element Method (FEM). He has made significant seminal contributions in the areas of finite element method, plate theory, solid mechanics, variational methods, mechanics of composites, functionally graded materials, fracture mechanics, plasticity, biomechanics, classical and non-Newtonian fluid mechanics, and applied functional analysis. Reddy has over 620 journal papers and 20 books and has given numerous national and international talks. He served as a member of the International Advisory Committee at ICTACEM, in 2001 and keynote addressing in 2014.[2][3]
A coupled map lattice (CML) is a dynamical system that models the behavior of non-linear systems. They are predominantly used to qualitatively study the chaotic dynamics of spatially extended systems. This includes the dynamics of spatiotemporal chaos where the number of effective degrees of freedom diverges as the size of the system increases.
Andrew Joseph Majda was an American mathematician and the Morse Professor of Arts and Sciences at the Courant Institute of Mathematical Sciences of New York University. He was known for his theoretical contributions to partial differential equations as well as his applied contributions to diverse areas including shock waves, combustion, incompressible flow, vortex dynamics, and atmospheric sciences. Majda was listed as an ISI highly cited researcher in mathematics.
NetworkX is a Python library for studying graphs and networks. NetworkX is free software released under the BSD-new license.
Valentin Afraimovich was a Soviet, Russian and Mexican mathematician. He made contributions to dynamical systems theory, qualitative theory of ordinary differential equations, bifurcation theory, concept of attractor, strange attractors, space-time chaos, mathematical models of non-equilibrium media and biological systems, travelling waves in lattices, complexity of orbits and dimension-like characteristics in dynamical systems.
Guanrong Chen (陈关荣) or Ron Chen is a Chinese mathematician who made contributions to Chaos theory. He has been the chair professor and the founding director of the Centre for Chaos and Complex Networks at the City University of Hong Kong since 2000. Prior to that, he was a tenured full professor at the University of Houston, Texas. Chen was elected Member of the Academy of Europe in 2014, elected Fellow of The World Academy of Sciences in 2015, and elected IEEE Fellow in 1997. He is currently the editor-in-chief for the International Journal of Bifurcation and Chaos.
Wassim Michael Haddad is a Lebanese-Greek-American applied mathematician, scientist, and engineer, with research specialization in the areas of dynamical systems and control. His research has led to fundamental breakthroughs in applied mathematics, thermodynamics, stability theory, robust control, dynamical system theory, and neuroscience. Professor Haddad is a member of the faculty of the School of Aerospace Engineering at Georgia Institute of Technology, where he holds the rank of Professor and Chair of the Flight Mechanics and Control Discipline. Dr. Haddad is a member of the Academy of Nonlinear Sciences for recognition of paramount contributions to the fields of nonlinear stability theory, nonlinear dynamical systems, and nonlinear control and an IEEE Fellow for contributions to robust, nonlinear, and hybrid control systems.
Jürgen Kurths is a German physicist and mathematician. He is senior advisor in the research department Complexity Sciences of the Potsdam Institute for Climate Impact Research, a Professor of Nonlinear Dynamics at the Institute of Physics at the Humboldt University, Berlin, and a 6th-century chair for Complex Systems Biology at the Institute for Complex Systems and Mathematical Biology at Kings College, Aberdeen University (UK). His research is mainly concerned with nonlinear physics and complex systems sciences and their applications to challenging problems in Earth system, physiology, systems biology and engineering.
Edward Ott is an American physicist most noted for his contributions to the development of chaos theory.
Ying-Cheng Lai is a Chinese theoretical physicist/electrical engineer who works in the field of chaos theory and complex dynamical systems. He is among the pioneers in the field of relativistic quantum chaos. Currently, he works at Arizona State University as a Regents Professor. He also holds an ISS Chair Professorship in Electrical Engineering.
Jack Kenneth Hale was an American mathematician working primarily in the field of dynamical systems and functional differential equations.
Soumitro Banerjee is an Indian electrical engineer and a professor at the Department of Physical Sciences of the Indian Institute of Science Education and Research, Kolkata. He is known for his studies on bifurcation phenomena in power electronic circuits and is an elected fellow of all three major Indian science academies: the National Academy of Sciences, India, Indian Academy of Sciences, and Indian National Science Academy. He is also a fellow of The World Academy of Sciences, Institute of Electrical and Electronics Engineers, West Bengal Academy of Sciences and the Indian National Academy of Engineering. The Council of Scientific and Industrial Research, the apex agency of the Government of India for scientific research, awarded him the Shanti Swarup Bhatnagar Prize for Science and Technology, one of the highest Indian science awards for his contributions to Engineering Sciences in 2003.
Sergej Flach is a theoretical physicist whose research has spanned a number of scientific fields in his career. With about 240 publications to his name, his research has been cited over 16,000 times giving him an h-index of 58 and i10-index of 174. He is a member of the American Physical Society, German Physical Society, Korean Physical Society, and New Zealand Institute of Physics. He is an editorial board member of Chaos (2016-) and was an editorial board member of Physical Review E (2009-2011).
Yamir Moreno is a professor of Physics at the Department of Theoretical Physics of the University of Zaragoza and Director of the Institute for Biocomputation and Physics of Complex Systems at the same institution.
Nikolay Vladimirovich Kuznetsov is a specialist in nonlinear dynamics and control theory.
