This research area generally covers dynamical systems and nonlinear dynamics, including such topics as coherent structures and nonlinear waves, chaos, and nonlinear dynamics. Focus for this area is on research by applied mathematicians, physicists, fluid dynamicists, engineers, and biologists in those areas of research.

Upcoming Related Conferences

Upcoming Related Conferences

HAPPENING VIRTUALLY: SIAM Conference on Applications of Dynamical Systems (DS21)

May 23 - 27, 2021 Originally scheduled in Portland, Oregon, U.S. More Information

Research Area Announcements

The Dynamical Systems Web

DSWeb, the online portal for SIAM’s dynamical systems activity group, is your source for up-to-date information on all aspects of dynamical systems and its applications.

Congratulations to the following two members of the SIAM community who will receive awards at the virtual SIAM Conference on Application of Dynamical Systems (DS21) . Additional information about ...

By Matthew R. Francis
The sight and smell of eutrophication—in the form of a layer of stinking green algae on a lake or pond—is likely familiar to many readers. The result is detrimental, ...

By Richard D. James , Alessia Nota , Gunjan Pahlani , and Juan J. L. Velázquez
Let \(A\) be any \(3 \times 3\) matrix, assume \(t\) is small enough that \(\det(I + tA)>0\), and consider ...

By David Lannes
“Consider the action of the waves — the ebb and flow of the tides. What is the ocean? A prodigious force wasted.” Back in 1874, when French writer Victor Hugo published his ...

By Kevin E. M. Church SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 745-783, January 2021. Moving averages and other functional forecasting models are used to inform policy in pandemic response....

By Yangyang Wang, Jeffrey P. Gill, Hillel J. Chiel, and Peter J. Thomas SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 701-744, January 2021. When dynamical systems that produce rhythmic behaviors operate within hard limits, they may exhibit limit...

By David J. Lloyd SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 671-700, January 2021. Stationary fronts connecting the trivial state and a cellular (distorted) hexagonal pattern in the Swift--Hohenberg...

By Hiroko Kamei and Haibo Ruan SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 636-670, January 2021. For a regular coupled cell network, synchrony subspaces are the polydiagonal subspaces that are invariant...

By Xiaoxian Tang and Hao Xu SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 608-635, January 2021. For three typical sets of small reaction networks (networks with two reactions, one irreversible and...

By Radouan Boukharfane , Julien Bodart , and Matteo Parsani
Computational fluid dynamics is a complex discipline that combines applied mathematics, physics, and computer science—and often ...

Mathematics and statistics play a vital part in everyday life. Mathematical and statistical techniques are used to help solve real-world problems, focusing on topics such as disease spread, ...

By Mattia Serra and L. Mahadevan
One of the grand challenges of modern biology is understanding the way in which a complex, multicellular organism arises from a single cell via ...

By Jan Bouwe van den Berg, Jean-Philippe Lessard, and Elena Queirolo SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 573-607, January 2021. In this paper we present a general approach to rigorously validate Hopf bifurcations as well...

By Matthieu Alfaro, Arnaud Ducrot, and Grégory Faye SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 571-572, January 2021. We are very grateful to Grégoire Nadin for bringing the following issue in the work...

By Alexandre A. P. Rodrigues SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 541-570, January 2021. We study the dynamics of the periodically forced May--Leonard system. We extend previous...

By Iacopo P. Longo, Carmen Nún͂ez, Rafael Obaya, and Martin Rasmussen SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 500-540, January 2021. An in-depth analysis of nonautonomous bifurcations of saddle-node type for scalar differential equations $x'=-x^2+q(t)\,x+p(t)$,...

By B. W. Qin, K. W. Chung, A. Algaba, and A. J. Rodríguez-Luis SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 403-437, January 2021. Based on the nonlinear time transformation method, in this paper we propose a recursive algorithm...

By Sarafa A. Iyaniwura and Michael J. Ward SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 438-499, January 2021. We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum-sensing and diffusion-mediated behavior...

By Kevin E. M. Church SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 745-783, January 2021. Moving averages and other functional forecasting models are used to inform policy in pandemic response....

By Yangyang Wang, Jeffrey P. Gill, Hillel J. Chiel, and Peter J. Thomas SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 701-744, January 2021. When dynamical systems that produce rhythmic behaviors operate within hard limits, they may exhibit limit...

By David J. Lloyd SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 671-700, January 2021. Stationary fronts connecting the trivial state and a cellular (distorted) hexagonal pattern in the Swift--Hohenberg...

By Hiroko Kamei and Haibo Ruan SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 636-670, January 2021. For a regular coupled cell network, synchrony subspaces are the polydiagonal subspaces that are invariant...

By Xiaoxian Tang and Hao Xu SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 608-635, January 2021. For three typical sets of small reaction networks (networks with two reactions, one irreversible and...

By Jan Bouwe van den Berg, Jean-Philippe Lessard, and Elena Queirolo SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 573-607, January 2021. In this paper we present a general approach to rigorously validate Hopf bifurcations as well...

By Matthieu Alfaro, Arnaud Ducrot, and Grégory Faye SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 571-572, January 2021. We are very grateful to Grégoire Nadin for bringing the following issue in the work...

By Alexandre A. P. Rodrigues SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 541-570, January 2021. We study the dynamics of the periodically forced May--Leonard system. We extend previous...

By Iacopo P. Longo, Carmen Nún͂ez, Rafael Obaya, and Martin Rasmussen SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 500-540, January 2021. An in-depth analysis of nonautonomous bifurcations of saddle-node type for scalar differential equations $x'=-x^2+q(t)\,x+p(t)$,...

By B. W. Qin, K. W. Chung, A. Algaba, and A. J. Rodríguez-Luis SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 403-437, January 2021. Based on the nonlinear time transformation method, in this paper we propose a recursive algorithm...

By Sarafa A. Iyaniwura and Michael J. Ward SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 438-499, January 2021. We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum-sensing and diffusion-mediated behavior...

By Takashi Teramoto and Peter van Heijster SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 371-402, January 2021. We use geometric singular perturbation techniques combined with an action functional approach to study traveling...

By B. A. J. de Wolff, F. Scarabel, S. M. Verduyn Lunel, and O. Diekmann SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 333-370, January 2021. Pseudospectral approximation reduces delay differential equations (DDE) to ordinary differential equations (ODE). Next one...

By Jason A. Otkin, Roland W. E. Potthast, and Amos S. Lawless SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 299-332, January 2021. In this study, we develop model bias estimators based on an asymptotic expansion of the...

By Adam Bauer and Paul Carter SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 262-298, January 2021. The one-fluid stellar wind problem for steady, radial outflow is considered, including effects of heat...

By Lu Lu, Xuhui Meng, Zhiping Mao, and George Em Karniadakis SIAM Review, Volume 63, Issue 1, Page 208-228, January 2021. Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has...

By Nicholas A. Battista SIAM Review, Volume 63, Issue 1, Page 181-207, January 2021. While students may find spline interpolation quite digestible based on their familiarity with the continuity of a function and...

By Bengt Fornberg SIAM Review, Volume 63, Issue 1, Page 167-180, January 2021. The trapezoidal rule uses function values at equispaced nodes. It is very accurate for integrals over periodic intervals, but...

By Nithin Govindarajan, Ryan Mohr, Shivkumar Chandrasekaran, and Igor Mezic SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 232-261, January 2021. The method of using periodic approximations to compute the spectral decomposition of the Koop- man...

By Michelle Feng and Mason A. Porter SIAM Review, Volume 63, Issue 1, Page 67-99, January 2021. A crucial step in the analysis of persistent homology is the transformation of data into an appropriate topological object...

By Juan Kuntz, Philipp Thomas, Guy-Bart Stan, and Mauricio Barahona SIAM Review, Volume 63, Issue 1, Page 3-64, January 2021. Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most...

By Nour Riman, Jonathan D. Victor, Sebastian D. Boie, and Bard Ermentrout SIAM Review, Volume 63, Issue 1, Page 100-120, January 2021. Animals use stereo sampling of odor concentration to localize sources and follow odor trails. We analyze the dynamics of...

By Xavier Allamigeon, Pascal Benchimol, Stéphane Gaubert, and Michael Joswig SIAM Review, Volume 63, Issue 1, Page 123-164, January 2021. Tropical geometry has been recently used to obtain new complexity results in convex optimization and game theory. In this...

By Misha E. Kilmer SIAM Review, Volume 63, Issue 1, Page 65-65, January 2021. We have two Research Spotlights papers in the lineup this issue. The first of these, “Persistent Homology of...

By Darinka Dentcheva SIAM Review, Volume 63, Issue 1, Page 165-166, January 2021. This issue of SIAM Review presents three papers in the Education section. The first paper, “Improving the Accuracy of...

By J. M. Sanz-Serna SIAM Review, Volume 63, Issue 1, Page 1-1, January 2021. The use of probabilistic ideas by applied mathematicians has seen a continued increase in recent decades. Probability now...

By The Editors SIAM Review, Volume 63, Issue 1, Page 121-121, January 2021. The SIGEST article in this issue is “What Tropical Geometry Tells Us about the Complexity of Linear Programming,” by...

By Volker H. Schulz SIAM Review, Volume 63, Issue 1, Page 231-245, January 2021. The section opens with a review well written by a giant in the field of numerical solution of partial...

By J. Sánchez Umbría and M. Net SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 208-231, January 2021. The thermal convection of rotating fluids in spherical geometry is a classical problem with application...

By François Baccelli and Thibaud Taillefumier SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 165-207, January 2021. Replica-mean-field models have been proposed to decipher the activity of otherwise analytically intractable neural networks...

By Jan Haskovec SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 130-148, January 2021. We present a simple proof of asymptotic consensus in the discrete Hegselmann--Krause model and flocking...

By Carlos García-Azpeitia, Wieslaw Krawcewicz, Manuel Tejada-Wriedt, and Haopin Wu SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 94-129, January 2021. In this paper we analyze nonlinear dynamics of the fullerene molecule. We prove, under...

By Qihuai Liu and Pedro J. Torres SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 149-164, January 2021. In this paper, we shall prove the stability of the particle advection around a fixed...

By Lars Gruene, Thomas Kriecherbauer, and Michael Margaliot SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 65-93, January 2021. The totally asymmetric simple exclusion process (TASEP) is a basic model of statistical mechanics that...

By Daozhi Han, Marco Hernandez, and Quan Wang SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 38-64, January 2021. In this article, we aim to classify the dynamic transitions and bifurcations for a family...

By Angélica Torres and Elisenda Feliu SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 1-37, January 2021. Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is,...

Congratulations to the following two members of the SIAM community who will receive awards at the virtual SIAM Conference on Application of Dynamical Systems (DS21) . Additional information about ...

By Matthew R. Francis
The sight and smell of eutrophication—in the form of a layer of stinking green algae on a lake or pond—is likely familiar to many readers. The result is detrimental, ...

By Richard D. James , Alessia Nota , Gunjan Pahlani , and Juan J. L. Velázquez
Let \(A\) be any \(3 \times 3\) matrix, assume \(t\) is small enough that \(\det(I + tA)>0\), and consider ...

By David Lannes
“Consider the action of the waves — the ebb and flow of the tides. What is the ocean? A prodigious force wasted.” Back in 1874, when French writer Victor Hugo published his ...

By Radouan Boukharfane , Julien Bodart , and Matteo Parsani
Computational fluid dynamics is a complex discipline that combines applied mathematics, physics, and computer science—and often ...

Mathematics and statistics play a vital part in everyday life. Mathematical and statistical techniques are used to help solve real-world problems, focusing on topics such as disease spread, ...

By Mattia Serra and L. Mahadevan
One of the grand challenges of modern biology is understanding the way in which a complex, multicellular organism arises from a single cell via ...

Established in 1967, the prize honors Norbert Wiener, a founder of the field of cybernetics. The prize is awarded every three years by SIAM and the American Mathematical Society (AMS) for an outstanding contribution to applied mathematics. Nominations can be submitted via the AMS website.

The Pioneer Prize is awarded every four years at the International Council for Industrial and Applied Mathematics (ICIAM) Congress to one individual for pioneering work introducing applied mathematical methods and scientific computing techniques to an industrial problem area or a new scientific field of applications. Nominations can be submitted via the ICIAM website.

The prize was established in 1999 in memory of Julian D. Cole and his work in mathematical applications to aerodynamics. It is awarded for the application of mathematical methods or the mathematical solution of a challenging problem in engineering or the physical or biological sciences.

The prize was established in 2011 to honor Martin David Kruskal for his many fundamental contributions, particularly the discovery and theory of solitons. It is awarded to one individual for a significant contribution to the mathematical theory of nonlinear waves and coherent structures.

The prize was established in 1986 in memory of Richard C. DiPrima, who served SIAM for many years and in 1979–1980 as SIAM President. It aims to recognize an early career researcher in applied mathematics and is based on the doctoral dissertation.

The prize was established in 2015 to honor T. Brooke Benjamin for his seminal contributions to nonlinear waves and coherent structures. It is awarded to a mid-career established researcher for recent work, based on publication in peer-reviewed journals.

Established by Idalia Reid in honor of her husband W. T. Reid and first awarded in 1994, the W. T. and Idalia Reid Prize in Mathematics is awarded annually in the broadly-defined areas of differential equations and control theory.

This joint prize was established in 2002 to honor Sonia Kovalevsky and her work on the theory of differential equations. It is awarded to anyone in the scientific or engineering community whose work highlights the achievements of women in applied and computational mathematics. Nominations can be submitted via the AWM website.

Established in 1967, the prize honors George David Birkhoff (1884-1944), who served as the American Mathematical Society (AMS) President during 1925-1926. The prize is awarded every three years by SIAM and AMS for an outstanding contribution to applied mathematics. Nominations can be submitted via the AMS website.

This prize was created in 2013 to emphasize George Pólya’s legacy of communicating mathematics effectively. It joins two long-standing Pólya prizes SIAM has awarded in combinatorics and other fields beginning in 1969.

Through the generosity and inspiration of Gerald and Judith Porter, the Mathematical Association of America (MAA), American Mathematical Society (AMS), and SIAM offer this annual lecture at the Joint Mathematics Meetings. The lecture, first awarded in 2010, is given on a mathematical topic accessible to the broader community.

Named in honor of I. E. Block, a co-founder and the first managing director of SIAM, this lecture is open to the public at the SIAM Annual Meeting. It is intended to encourage public appreciation of applied mathematics and computational science by reaching out to the local community.

The prize was established in 2000 in memory of John David Crawford and his contributions to the physics of collisionless plasmas and pattern formation. It is awarded to one individual for recent work on a topic in nonlinear science, based on publication in peer-reviewed journals.

Established in 1959, the prize honors John von Neumann, a founder of modern computing. The prize is awarded annually for distinguished contributions to applied mathematics and for the effective communication of these ideas to the community.

The JPBM Communications Award is given annually to reward and encourage communicators who, on a sustained basis, bring mathematical ideas and information to non-mathematical audiences. The prize may be awarded in two categories: For Public Outreach and For Expository and Popular Books. Nominations can be submitted via the AMS website.

The prize was established in 2000 in memory of Jürgen Moser, a leading mathematician who helped develop influential theories in celestial mechanics and dynamical systems theory. It is awarded to one individual who has made distinguished contributions to nonlinear science.

Established in 1998 in memory of Ralph E. Kleinman, the prize recognizes contributions that bridge the gap between high-level mathematics and engineering problems. The award is based on the quality and impact of the mathematics.

The Red Sock Award is given for the best poster presentation by a student or postdoc at the SIAM Conference on Applications of Dynamical Systems. Four awards are made each prize cycle. By tradition, each recipient is awarded a red sock.

The prize recognizes students for outstanding solutions to real world math problems. It is awarded to two of the teams judged "Outstanding" in the Mathematical Contest in Modeling (MCM) administered annually by the Consortium for Mathematics and Its Applications (COMAP). Registration is accepted via the COMAP website.

The SIAM Outstanding Paper Prize is not currently active. For the 20 years before it was discontinued in 2019, the SIAM Outstanding Paper Prizes brought attention to papers published in SIAM journals. Three awards were made each year to the authors of papers deemed by SIAM journal editors-in-chief worthy of particular attention.

The prize, established in 1985 and originally intended to be awarded periodically, is now awarded annually for contributions to the advancement of applied mathematics on the national or international level.

The SIAM Student Paper Prize is awarded annually to the student author(s) of the most outstanding paper(s) accepted by SIAM journals within the three years preceding the nomination deadline. Starting with the 2018 award, the focus of the prize is to recognize outstanding scholarship by students in SIAM journals.

This prize was established in 1968 to commemorate Theodore von Kármán and his work in aerodynamics. It is awarded every five years for a notable application of mathematics to mechanics or engineering in the five to ten years preceding the award.

This activity group provides a forum for the exchange of ideas and information between mathematicians and applied scientists whose work involves dynamical systems. The goal of this group is to facilitate the development and application of new theory and methods of dynamical systems. The techniques in this area are making major contributions in many areas, including biology, nonlinear optics, fluids, chemistry, and mechanics.

This activity group fosters collaborations among applied mathematicians, physicists, fluid dynamicists, engineers, and biologists in those areas of research related to the theory, development, and use of nonlinear waves and coherent structures. It promotes and facilitates nonlinear waves and coherent structures as an academic discipline; brokers partnerships between academia, industry, and government laboratories; and works with other professional societies to promote nonlinear waves and coherent structures.

SIAM Journal on Applied Dynamical Systems (SIADS) publishes research articles that concentrate on the mathematical analysis and modeling of dynamical systems and its application to the physical, engineering, life, and social sciences. SIADS highly emphasizes the use of color, animated visualizations, and internal linking to enhance the exposition, however, papers without these enhancements are accepted as well.

Multiscale Modeling & Simulation
SIAM J. on Applied Algebra and Geometry
SIAM J. on Applied Dynamical Systems
SIAM J. on Applied Mathematics
SIAM J. on Computing
SIAM J. on Control and Optimization
SIAM J. on Discrete Mathematics
SIAM J. on Financial Mathematics
SIAM J. on Imaging Sciences
SIAM J. on Mathematical Analysis
SIAM J. on Matrix Analysis and Applications
SIAM J. on Numerical Analysis
SIAM J. on Optimization
SIAM J. on Scientific Computing
SIAM/ASA J. on Uncertainty Quantification
SIAM Review
Theory of Probability & Its Applications

General Opportunities

We know it can be overwhelming to keep track of career opportunities that may be relevant to you as a member of the SIAM community. So, we’ve compiled lists of some of our favorite fellowship, internship, and research opportunities. Check ‘em out!

Fellowships

Looking for financial support to further your research? Fellowships often provide funding plus experiential learning opportunities to young researchers. Learn more about fellowship opportunities.

Internships allow you to network and forge connections for future job possibilities, while also exploring possible areas of interest. Look at this list of companies who offer valuable opportunities.

Our community is founded on igniting groundbreaking developments in applied math and computational science. Take a deeper dive into your area of study with one of these opportunities.