Delay Differential Equations: Theory, Control and Applications

Dear Colleagues,

Delay differential equations (DDEs) represent critical systems in which temporal lags between causes and effects induce rich yet complex dynamics. These models arise naturally in domains such as neuroscience, ecology, economics, and control engineering, where time delays capture memory effects, propagation latencies, or decision-making processes. As modern systems grow in complexity, DDEs will be a vital tool for understanding nonlinear phenomena and designing robust control strategies.

This Special Issue seeks to advance DDE research by bridging theoretical rigor and practical applications. Theoretical explorations may address stability criteria, bifurcation analysis, and numerical methods for approaching DDEs with state-dependent delays. Control-oriented studies could propose novel predictor-based feedback laws, adaptive control frameworks, or machine learning-driven delay compensation techniques. Applied research should demonstrate DDEs' ability to model real-world systems, such as physiological regulatory networks, power grids with delayed feedback, or economic models with investment lags.

We particularly encourage interdisciplinary submissions integrating DDEs with soft computing paradigms, e.g., using fuzzy logic for uncertain delays, granular computing for complex dynamics, or evolutionary algorithms for parameter estimation. Topics of interest include the stability of DDEs, optimal control under communication delays, deep learning architectures for delay identification, and the application of DDE-based models in epidemiology or finance.

We invite researchers to submit high-quality, original work, including theoretical breakthroughs, algorithmic innovations, and case studies with measurable impacts. Contributions will be peer-reviewed and selected based on their novelty, methodological rigor, and relevance to the emerging challenges regarding DDEs.

We look forward to receiving your groundbreaking submissions.

Prof. Dr. Changyou Wang
Dr. Zacharias A. Anastassi
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• delay differential equations (DDEs)
• stability criteria
• bifurcation analysis
• numerical methods
• predictive feedback control
• adaptive control frameworks
• machine learning-driven delay compensation
• physiological regulatory networks
• power grid dynamics with delayed feedback
• epidemiological/financial DDE modeling