In mathematics, a heteroclinic network is an invariant set in the phase space of a dynamical system. It can be thought of loosely as the union of more than one heteroclinic cycle. Heteroclinic networks arise naturally in a number of different types of applications, including fluid dynamics and populations dynamics.
Harry Leonard Swinney is an American physicist noted for his contributions to the field of nonlinear dynamics.
Amir Ordacgi Caldeira is a Brazilian physicist. He received his bachelor's degree in 1973 from the Pontifícia Universidade Católica do Rio de Janeiro, his M.Sc. degree in 1976 from the same university, and his Ph.D. in 1980 from University of Sussex. His Ph.D. advisor was the Physics Nobel Prize winner Anthony James Leggett. He joined the faculty at Universidade Estadual de Campinas (UNICAMP) in 1980. In 1984 he did post-doctoral work at the Kavli Institute for Theoretical Physics (KITP) at University of California, Santa Barbara and at the Thomas J. Watson Research Laboratory at IBM. In 1994–1995 he spent a sabbatical at the University of Illinois at Urbana-Champaign. He is currently a full professor at Universidade Estadual de Campinas. He was the recipient of the Wataghin Prize, from Universidade Estadual de Campinas, for his contributions to theoretical physics in 1986.
Dissipative solitons (DSs) are stable solitary localized structures that arise in nonlinear spatially extended dissipative systems due to mechanisms of self-organization. They can be considered as an extension of the classical soliton concept in conservative systems. An alternative terminology includes autosolitons, spots and pulses.
Quantum dimer models were introduced to model the physics of resonating valence bond (RVB) states in lattice spin systems. The only degrees of freedom retained from the motivating spin systems are the valence bonds, represented as dimers which live on the lattice bonds. In typical dimer models, the dimers do not overlap.
Patrick A. Lee is a professor of physics at the Massachusetts Institute of Technology (MIT).
A coupled map lattice (CML) is a dynamical system that models the behavior of nonlinear 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.
Daniel L. Stein is an American physicist and Professor of Physics and Mathematics at New York University. From 2006 to 2012 he served as the NYU Dean of Science.
Cybernetical physics is a scientific area on the border of cybernetics and physics which studies physical systems with cybernetical methods. Cybernetical methods are understood as methods developed within control theory, information theory, systems theory and related areas: control design, estimation, identification, optimization, pattern recognition, signal processing, image processing, etc. Physical systems are also understood in a broad sense; they may be either lifeless, living nature or of artificial (engineering) origin, and must have reasonably understood dynamics and models suitable for posing cybernetical problems. Research objectives in cybernetical physics are frequently formulated as analyses of a class of possible system state changes under external (controlling) actions of a certain class. An auxiliary goal is designing the controlling actions required to achieve a prespecified property change. Among typical control action classes are functions which are constant in time, functions which depend only on time, and functions whose value depends on measurement made at the same time or on previous instances. The last class is of special interest since these functions correspond to system analysis by means of external feedback.
Eric R. Weeks is an American physicist. He completed his B.Sc. at the University of Illinois at Urbana–Champaign in 1992. He obtained a Ph.D. in physics from the University of Texas at Austin in 1997, working under Harry Swinney, and later completed post-doctoral research with David Weitz and Arjun Yodh at Harvard University and the University of Pennsylvania. He is currently a full professor at Emory University in Atlanta, Georgia.
In physical cosmology, warm inflation is one of two dynamical realizations of cosmological inflation. The other is the standard scenario, sometimes called cold inflation.
Miguel Angel Fernández Sanjuán is a Spanish Theoretical Physicist from Leon, Spain. He is known for his contributions in nonlinear dynamics, chaos theory, and control of chaos, and has published several scientific papers and popular news articles. He has supervised around 20 PhD students in Nonlinear Dynamics, Chaos and Complex Systems.
Oreste Piro is a dynamical systems theorist and biophysicist. He is at the Universitat de les Illes Balears (UIB) in Palma de Mallorca.
In applied mathematics and astrodynamics, in the theory of dynamical systems, a crisis is the sudden appearance or disappearance of a strange attractor as the parameters of a dynamical system are varied. This global bifurcation occurs when a chaotic attractor comes into contact with an unstable periodic orbit or its stable manifold. As the orbit approaches the unstable orbit it will diverge away from the previous attractor, leading to a qualitatively different behaviour. Crises can produce intermittent behaviour.
Chaotic scattering is a branch of chaos theory dealing with scattering systems displaying a strong sensitivity to initial conditions. In a classical scattering system there will be one or more impact parameters, b, in which a particle is sent into the scatterer. This gives rise to one or more exit parameters, y, as the particle exits towards infinity. While the particle is traversing the system, there may also be a delay time, T—the time it takes for the particle to exit the system—in addition to the distance travelled, s. In certain systems the two will be equivalent—see below. In a chaotic scattering system, a minute change in the impact parameter, may give rise to a very large change in the exit parameters.
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.
Celso Grebogi is a Brazilian theoretical physicist who works in the area of chaos theory. He is one among the pioneers in the nonlinear and complex systems and chaos theory. Currently he works at the University of Aberdeen as the "Sixth Century Chair in Nonlinear and Complex Systems". He has done extensive research in the field of plasma physics before his work on the theory of dynamical systems. He and his colleagues have shown with a numerical example that one can convert a chaotic attractor to any one of numerous possible attracting time-periodic motions by making only small time-dependent perturbations of an available system parameter. This article is considered as one among the classic works in the control theory of chaos and their control method is known as the OGY method. He was listed in the 2016 Thomson Reuters Citation Laureates.
In mathematics, a strange nonchaotic attractor (SNA) is a form of attractor which, while converging to a limit, is strange, because it is not piecewise differentiable, and also non-chaotic, in that its Lyapunov exponents are non-positive. SNAs were introduced as a topic of study by Grebogi et al. in 1984. SNAs can be distinguished from periodic, quasiperiodic and chaotic attractors using the 0-1 test for chaos.
Physics of financial markets is a non-orthodox economics discipline that studies financial markets as physical systems. It seeks to understand the nature of financial processes and phenomena by employing the scientific method and avoiding beliefs, unverifiable assumptions and immeasurable notions, not uncommon to economic disciplines.
In mathematics, the Kuramoto–Sivashinsky equation is a fourth-order nonlinear partial differential equation. It is named after Yoshiki Kuramoto and Gregory Sivashinsky, who derived the equation in the late 1970s to model the diffusive–thermal instabilities in a laminar flame front. It was later and independently derived by G. M. Homsy and A. A. Nepomnyashchii in 1974, in connection with the stability of liquid film on an inclined plane and by R. E. LaQuey et. al. in 1975 in connection with trapped-ion instability. The Kuramoto–Sivashinsky equation is known for its chaotic behavior.
