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Discrete and Continuous Dynamical Systems

American Institute of Mathematical Sciences

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About Discrete and Continuous Dynamical Systems

Overview

Discrete and Continuous Dynamical Systems (often abbreviated DCDS, and known as Series A of the DCDS family) is a peer-reviewed mathematics journal published by the American Institute of Mathematical Sciences (AIMS), based in Springfield, Missouri, United States. Founded in 1996, it is the flagship journal of AIMS and one of the principal international venues for research on dynamical systems, differential equations, and the analysis that underpins them.

The journal publishes high-quality original papers and invited expository papers on the theory and methods of analysis, differential equations, and dynamical systems. Its editorial standard, as stated by the publisher, is demanding: to appear in the journal, an original paper must be correct, new, nontrivial, and of interest to a substantial number of readers — and the journal aims to be the record of important new results in its field, maintaining the highest standards of innovation and quality.

DCDS appears monthly and operates on a hybrid publishing model, combining subscription access with open-access options. It carries the print ISSN 1078-0947 and the electronic ISSN 1553-5231. In citation databases it is a consistent Q1 performer, ranked in the top quartile in Analysis, Applied Mathematics, and Discrete Mathematics and Combinatorics, with an SJR around 1.07 and a Scopus H-index near 80.

Over nearly three decades, DCDS has grown from a single journal into the anchor of a family of AIMS serials: DCDS-B (launched 2001, focused on interdisciplinary mathematical modeling and scientific computation), DCDS-S (launched 2008), and, most recently, DCDS-I and DCDS-C (both launched 2025, devoted to intelligence/AI and AI-for-science themes). The original journal continues as Series A, the core outlet for fundamental work in dynamics and differential equations.

History

Discrete and Continuous Dynamical Systems was founded in 1996 by the American Institute of Mathematical Sciences, a mathematical sciences publisher headquartered at P.O. Box 2604, Springfield, MO 65801, USA. Scopus and SCImago coverage records confirm continuous coverage from 1996 onward, and the journal has published without interruption ever since.

The journal's launch filled a clear need: a dedicated, high-standard venue for the then rapidly growing fields of dynamical systems theory, nonlinear analysis, and differential equations. Its early volumes established the template — rigorous papers on analysis, differential equations, and dynamics, including invited expository articles that surveyed fast-moving subfields.

As the field expanded, so did the DCDS family. In 2001, AIMS launched Discrete and Continuous Dynamical Systems – Series B (DCDS-B), a sister journal centered on the interdisciplinary interactions between mathematical modeling, analysis, and scientific computation, with a mission to bridge mathematics and the sciences. In 2008, DCDS-S (Series S) followed. In 2025, AIMS introduced two further series — DCDS-I (Intelligence) and DCDS-C (AI for Science) — dedicated to research at the intersection of dynamical systems, artificial intelligence, machine learning, and computational neuroscience. Through all of this growth, the original journal has remained Series A: the home of the core theory and methods of analysis, differential equations, and dynamical systems.

Editorially, the journal has been led over the years by prominent figures in dynamical systems and PDEs. AIMS records note, for example, that Alessio Figalli served as a Managing Editor from 2012 to 2016. The current Editor in Chief is Shouchuan Hu of Missouri State University, as listed on AIMS's official journal contacts page.

Aims and Scope

Known as Series A of DCDS, the journal publishes peer-reviewed, high-quality original papers alongside invited expository papers dealing with the theory and methods of analysis, differential equations, and dynamical systems. It presents itself as the record for important new results in these fields, committed to the highest standards of innovation and quality. An original submission is expected to be correct, new, and nontrivial, and to interest a substantial readership — a bar the journal has maintained across its three decades.

The journal's published output, as classified by OpenAlex topic modeling, concentrates on:

  • Mathematical analysis — the largest share of the journal's content, including nonlinear analysis and functional-analytic methods.
  • Pure mathematics with dynamical flavor — ergodic theory, topological dynamics, and related structures.
  • Combinatorics and discrete dynamics — discrete dynamical systems, difference equations, and combinatorial methods.
  • Nonlinear systems and differential equations — ordinary, partial, and functional differential equations; bifurcation theory; stability and attractors.
  • Applied and computational themes — numerical analysis of dynamical models, including widely cited work on phase-field equations.

The journal complements its regular monthly issues with special issues on emerging topics, and it maintains "Most Viewed" and "Most Cited" features on its AIMS journal page, reflecting its emphasis on both scholarly influence and readership.

Editorial Leadership

According to the American Institute of Mathematical Sciences' official journal contacts page, the Editor in Chief of Discrete and Continuous Dynamical Systems is Shouchuan Hu (Missouri State University, USA).

The journal's official editorial-board page additionally lists Managing Editors — including editors based at the University of Bath (UK), whose interests cover nonlinear elliptic and parabolic equations, and at the University of British Columbia (Canada), whose interests cover concentration phenomena and reaction–diffusion systems — though individual names did not render in the publicly accessible page snapshot consulted for this profile and are therefore not reproduced here. AIMS also records past editorial service, such as Alessio Figalli's term as Managing Editor from 2012 to 2016.

Researchers should confirm the current full board on the journal's official editorial-board page (aimsciences.org/DCDS/editorialboard) before submitting, since board composition changes over time.

Key Facts

  • Journal title: Discrete and Continuous Dynamical Systems (DCDS — Series A)
  • Standard abbreviation: Discrete Contin. Dyn. Syst. / Discret. Contin. Dyn. Syst.
  • ISSN (print): 1078-0947
  • eISSN (online): 1553-5231
  • Publisher: American Institute of Mathematical Sciences (AIMS), P.O. Box 2604, Springfield, MO 65801-2604, USA
  • Country of publication: United States
  • Founded: 1996 (continuous publication since)
  • Publication frequency: Monthly — 12 issues per year
  • Language: English
  • Publishing model: Hybrid (per AIMS's official journal page)
  • Submission system: AIMS EditFlow (ef.msp.org), linked as "Submit a Paper" from the official journal page
  • SCImago metrics: SJR ~1.07; H-index ~80; Q1 in Analysis, Applied Mathematics, and Discrete Mathematics and Combinatorics
  • OpenAlex metrics: 5,572 works; 80,988 citations; H-index 92; i10-index 2,196; 2-year mean citedness ~0.99
  • Sister journals: DCDS-B (2001), DCDS-S (2008), DCDS-I (2025), DCDS-C (2025)

Indexing and Abstracting

Discrete and Continuous Dynamical Systems is indexed in Scopus — where it holds Q1 rankings in Analysis, Applied Mathematics, and Discrete Mathematics and Combinatorics — and in the Web of Science Science Citation Index Expanded (SCIE), under which it receives a Journal Impact Factor (recent metric aggregators place it in the low-1s, e.g., around 1.1). AIMS states that its DCDS titles are indexed in Mathematical Reviews/MathSciNet, SCIE, Scopus, zbMATH Open, and additional services, per the publisher's official journal flyers.

The journal's metadata is aggregated by OpenAlex and Crossref, which registers its article DOIs under the publisher's 10.3934 prefix (e.g., 10.3934/dcds.2010.28.1669). Authors with funder or institutional mandates tied to particular indexes should confirm current coverage with the index provider or the publisher.

Landmark Papers

The following papers, each verified individually through the Crossref API, rank among the most cited articles the journal has published. DOIs link to the definitive versions.

1. Shen & Yang (2010) — Numerical approximations of Allen–Cahn and Cahn–Hilliard equations

DOI: 10.3934/dcds.2010.28.1669

Jie Shen and Xiaofeng Yang developed energy-stable numerical schemes for the Allen–Cahn and Cahn–Hilliard phase-field equations, models central to materials science and interface dynamics. With several hundred citations, it is one of the most cited papers in the journal's history and a standard reference for stable time-stepping methods in phase-field simulation.

2. Servadei & Valdinoci (2013) — Variational methods for non-local operators of elliptic type

DOI: 10.3934/dcds.2013.33.2105

Raffaella Servadei and Enrico Valdinoci built a variational framework for non-local (fractional-type) elliptic operators, providing the functional-analytic foundations — function spaces, embeddings, and existence theory — on which much of the subsequent literature on fractional elliptic problems rests. It is among the journal's most cited contributions of the 2010s.

3. Ball (2004) — Global attractors for damped semilinear wave equations

DOI: 10.3934/dcds.2004.10.31

J. M. Ball studied the existence and structure of global attractors for damped semilinear wave equations, a core topic in infinite-dimensional dynamical systems. The paper's treatment of attractors for hyperbolic dynamics has been widely cited in the long-time-behavior literature.

Open Access and APCs

DCDS operates on a hybrid publishing model, as stated on AIMS's official journal page: the journal is primarily subscription-based, with open-access publication options available to authors. AIMS journals commonly offer authors the choice of publishing open access for a fee, or publishing under the standard subscription model at no charge to the author.

No specific article processing charge (APC) figure for DCDS is publicly listed in the sources consulted for this profile. Authors considering the open-access route should consult AIMS's current author instructions or contact the publisher for the applicable APC, available waivers or discounts, and the exact licensing terms (AIMS open-access articles are typically published under Creative Commons licenses).

Submission Information

Manuscripts are submitted through AIMS EditFlow, the publisher's online submission and peer-review system, reached via the "Submit a Paper" link on the journal's official page (aimsciences.org/DCDS), which directs to ef.msp.org. Editorial correspondence — for questions about submission status or refereeing — is directed to the journal editors through the contacts listed on AIMS's official journal contacts page.

Given the journal's stated editorial bar — original papers must be correct, new, nontrivial, and of interest to a substantial number of readers — authors should ensure their manuscript makes a clear, substantive contribution to analysis, differential equations, or dynamical systems before submitting. Invited expository papers are handled by editorial invitation. As always, consult the current AIMS author guidelines for formatting, reference style, and article-type requirements before submission.

Frequently Asked Questions

What is the ISSN of Discrete and Continuous Dynamical Systems?

Print ISSN 1078-0947; electronic ISSN 1553-5231.

Who publishes Discrete and Continuous Dynamical Systems?

The American Institute of Mathematical Sciences (AIMS), based in Springfield, Missouri, USA.

What is the difference between DCDS, DCDS-A, DCDS-B, and DCDS-S?

The original journal, founded in 1996, is now designated Series A — the core journal for analysis, differential equations, and dynamical systems. DCDS-B (2001) focuses on interdisciplinary mathematical modeling and scientific computation; DCDS-S (2008) is a companion series; DCDS-I and DCDS-C (both 2025) cover intelligence/AI and AI-for-science topics.

When was the journal founded?

1996, with continuous publication since.

How frequently is it published?

Monthly, 12 issues per year.

Who is the Editor in Chief?

Shouchuan Hu (Missouri State University), per AIMS's official journal contacts page.

Is Discrete and Continuous Dynamical Systems peer-reviewed?

Yes. It is a peer-reviewed journal applying a demanding standard: published original papers must be correct, new, nontrivial, and of interest to a substantial readership.

Is it open access?

It is a hybrid journal — subscription-based with open-access options for authors. No public APC figure was found; confirm current charges with AIMS.

What are the journal's metrics?

SCImago records an SJR of about 1.07 and an H-index near 80, with Q1 rankings in Analysis, Applied Mathematics, and Discrete Mathematics and Combinatorics. OpenAlex records 5,572 works, 80,988 citations, and an H-index of 92. The journal is also tracked in Journal Citation Reports (SCIE). Always check the source and year of any metric before citing it.

Where do I submit a manuscript?

Through AIMS EditFlow via the "Submit a Paper" link on the official journal page at aimsciences.org/DCDS.

AIMS and the DCDS Family of Journals

The American Institute of Mathematical Sciences (AIMS) is a US-based publisher of mathematical sciences journals, headquartered at P.O. Box 2604, Springfield, Missouri 65801. AIMS operates a focused portfolio of mathematics titles, and Discrete and Continuous Dynamical Systems is its flagship — the journal around which the publisher's reputation was built.

AIMS's other journals, as listed on the publisher's official contacts page, include Communications on Pure and Applied Analysis (CPAA, Editor in Chief Shouchuan Hu), Evolution Equations and Control Theory (EECT, Editor in Chief Irena Lasiecka), Inverse Problems and Imaging (IPI, Editor in Chief Gang Bao), Discrete and Continuous Dynamical Systems – B (DCDS-B, Editors in Chief Yuan Lou and Michael Winkler), and Discrete and Continuous Dynamical Systems – S (DCDS-S, Editors in Chief Xiaoying Han and Alain Miranville). The concentration of leading figures in PDEs, control theory, and dynamical systems across these mastheads reflects AIMS's editorial strategy: journals led by active researchers in the fields they cover.

Within this portfolio, the DCDS family itself has a clear division of labor, documented in AIMS's official journal flyers:

  • DCDS (Series A) — the original journal (1996): theory and methods of analysis, differential equations, and dynamical systems; monthly; hybrid; ISSN 1078-0947 / eISSN 1553-5231.
  • DCDS-B (2001) — interdisciplinary: mathematical modeling, analysis, and scientific computation bridging mathematics and the sciences; monthly; ISSN 1531-3492 / eISSN 1553-524X; 2025 Impact Factor 1.4 and CiteScore 2.9 per AIMS's official flyer.
  • DCDS-S (2008) — companion series; ISSN 1937-1632 / eISSN 1937-1179; Q2 in its Scopus categories.
  • DCDS-I (2025) — "Intelligence": dynamical systems meets AI, machine learning, and computational neuroscience; quarterly from 2026; eISSN 3071-4516.
  • DCDS-C (2025) — "AI for Science": dynamical systems and AI for scientific discovery; 2 issues in 2025, quarterly from 2026.

Authors should take care to submit to the correct series: a theoretical paper on attractors belongs in Series A, while a paper on data-driven modeling of a biological system likely belongs in DCDS-B. The series share a publisher and a name but have separate editorial boards, ISSNs, and metrics.

Standing and Citation Profile

DCDS Series A is one of the stronger performers among specialist mathematics journals. SCImago places it in Q1 in all three of its subject categories — Analysis, Applied Mathematics, and Discrete Mathematics and Combinatorics — with an SJR of approximately 1.07 and a Scopus H-index near 80. Journal Citation Reports tracks it under the Science Citation Index Expanded, with recent aggregator figures putting its Impact Factor in the low 1s (around 1.1 for 2024).

OpenAlex paints a consistent picture at larger scale: 5,572 works, 80,988 citations, an H-index of 92, an i10-index of 2,196, and a two-year mean citedness of 0.99 — roughly one citation per recent paper per year, a healthy rate for a theoretical mathematics journal. The journal's most cited papers, such as Shen–Yang on phase-field numerics and Servadei–Valdinoci on non-local operators, show how Series A captures both core theory and computationally relevant analysis.

The journal actively curates its visibility through special issues on emerging topics and through "Most Viewed" and "Most Cited" features on its AIMS page — mechanisms that help important papers find readers beyond the specialist community. Its monthly cadence (12 issues per year) gives it one of the higher publication volumes among theory-oriented dynamics journals, with annual article counts in the low hundreds.

Sources

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