Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
2.2
1.5
Journals
Modelling
Special Issues
Modelling of Nonlinear Dynamical Systems
share announcement

Modelling of Nonlinear Dynamical Systems

A special issue of Modelling (ISSN 2673-3951).

Deadline for manuscript submissions: 31 March 2026 | Viewed by 2015

Special Issue Editors

Prof. Dr. Liming Dai

E-Mail Website
Guest Editor
Industrial Systems Engineering, University of Regina, Regina, SK S4S 0A2, Canada
Interests: nonlinear dynamics; numerical methods and simulations of nonlinear dynamic systems; diagnosis of nonlinear characteristics; response prediction of nonlinear systems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jialin Tian

E-Mail Website
Guest Editor
School of Mechanical Engineering, Southwest Petroleum University, Chengdu 610500, China
Interests: dynamics and control; modern design of oil and gas equipment; underground tools and drill bit technology; underground testing and intelligent control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue explores the latest advancements in nonlinear dynamical system modeling. It aims to highlight innovative research and practical applications that leverage nonlinear dynamical system modeling in order to enhance the understanding, analysis, prediction, and control of complex systems. This Special Issue seeks to provide valuable insights for researchers, practitioners, and industry professionals dedicated to deepening their insights into complex phenomena and developing effective solutions through cutting-edge nonlinear dynamical system modeling techniques.

Prof. Dr. Liming Dai
Prof. Dr. Jialin Tian
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Modelling is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 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.

Keywords

  • nonlinear dynamical systems
  • data-driven modeling
  • first-principle modeling
  • system identification
  • system control
  • complex systems
  • chaos
  • machine learning

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

26 pages, 4189 KB  
Article
A Novel PID-LQR Controller Scheme to Enhance the Performance of Full-Bridge Boost Converter
by Sulistyo Wijanarko, Rina Ristiana and Anwar Muqorobin
Modelling 2026, 7(2), 51; https://doi.org/10.3390/modelling7020051 - 6 Mar 2026
Abstract
PID (proportional integral derivative) control has been widely used in industry due to its simplicity in implementation and satisfactory performance. However, the controller tuning is very troublesome when used in complex and nonlinear systems. The full bridge boost converter (FBBC) is a nonlinear [...] Read more.
PID (proportional integral derivative) control has been widely used in industry due to its simplicity in implementation and satisfactory performance. However, the controller tuning is very troublesome when used in complex and nonlinear systems. The full bridge boost converter (FBBC) is a nonlinear system, so the PID control application in this converter should be further explored. This paper introduces a control approach that integrates PID control with a Linear Quadratic Regulator (LQR) for FBBC. To enable linear control design, the FBBC is linearized around its steady state operating points. The control architecture is structured into four cases: Case 1: PI-LQR Output Feedback, Case 2: PI-LQR State Feedback, Case 3: PID-LQR Output Feedback, and Case 4: PID-LQR State Feedback. The analysis aims to identify the most reliable system performance under input voltage change and load variation. The simulation results indicate that under the input voltage and load changes, cases 2 and 4 produce faster settling times, each with a settling time of 0.025 s and 0.015 s, respectively. However, both controllers produce negligible steady state error (less than 1%). Overall, Case 4 (PID-LQR State Feedback) consistently delivers the best performance, characterized by faster settling time, negligible steady state error, optimal control signal, and significantly reduced oscillation in both the inductor current and output voltage. Full article
(This article belongs to the Special Issue Modelling of Nonlinear Dynamical Systems)
►▼ Show Figures

Figure 1

15 pages, 2836 KB  
Article
Winding Numbers in Discrete Dynamics: From Circle Maps and Fractals to Chaotic Poincaré Sections
by Zhengyuan Zhang, Liming Dai and Na Jia
Modelling 2025, 6(4), 148; https://doi.org/10.3390/modelling6040148 - 14 Nov 2025
Viewed by 623
Abstract
Winding numbers are key indices in the depiction, modelling, and testing of dynamical processes. They capture phase progression on closed curves and are robust for quasiperiodic dynamics, but their status for chaotic Poincaré sections is unclear. This study tests whether any non-trivial winding-type [...] Read more.
Winding numbers are key indices in the depiction, modelling, and testing of dynamical processes. They capture phase progression on closed curves and are robust for quasiperiodic dynamics, but their status for chaotic Poincaré sections is unclear. This study tests whether any non-trivial winding-type index can be extracted from chaotic Poincaré maps using three approaches: (i) phase-angle analysis, (ii) Kabsch optimal-rotation estimation, and (iii) local turning-angle averaging. To benchmark feasibility and error, we compare four systems: the standard circle map, the same circle map embedded on two planar fractal curves (Koch snowflake and Hilbert curve), a quasiperiodic Duffing–van der Pol (DVP) Poincaré map, and a chaotic DVP Poincaré map. For the quasiperiodic map, all methods yield consistent, accurate winding numbers. For the transitional systems (circle map and its fractal embeddings), indices remain non-trivial but more deviated. In stark contrast, chaotic Poincaré maps produce only trivial indices across all methods. These results indicate a crucial fact about the modelling of chaotic Poincaré maps. That is, although being fractal, they are not merely chaotic maps on fractal curves; rather, they reflect a tighter coupling of geometry and dynamics. Practically, the recoverability of a non-trivial winding index offers a simple diagnostic to distinguish quasiperiodicity from chaos in Poincaré data or corresponding models. The constructed chaotic-map-on-fractal systems also act as test-bed models that bridge ideal one-dimensional mappings and realistic two-dimensional Poincaré sections. Full article
(This article belongs to the Special Issue Modelling of Nonlinear Dynamical Systems)
►▼ Show Figures

Figure 1

15 pages, 1487 KB  
Article
Model-Free Identification of Heat Exchanger Dynamics Using Convolutional Neural Networks
by Mario C. Maya-Rodriguez, Ignacio Carvajal-Mariscal, Mario A. Lopez-Pacheco, Raúl López-Muñoz and René Tolentino-Eslava
Modelling 2025, 6(4), 127; https://doi.org/10.3390/modelling6040127 - 14 Oct 2025
Viewed by 813
Abstract
Heat exchangers are widely used process equipment in industrial sectors, making the study of their temperature dynamics particularly appealing due to the nonlinearities involved. Model-free approaches enable the use of input and output data to generate specific and accurate estimations for each proposed [...] Read more.
Heat exchangers are widely used process equipment in industrial sectors, making the study of their temperature dynamics particularly appealing due to the nonlinearities involved. Model-free approaches enable the use of input and output data to generate specific and accurate estimations for each proposed system. In this work, a model-free identification strategy is proposed using a convolutional neural network to estimate the system’s behavior. Notably, the model does not rely on direct temperature measurements; instead, temperature is inferred from other system signals such as reference, flow, and control inputs. This data-driven approach offers greater specificity and adaptability, often outperforming manufacturer-provided coefficients whose performance may vary from design expectations. The results yielded an R2 index of 0.9951 under nominal conditions and 0.9936 when the system was subjected to disturbances. Full article
(This article belongs to the Special Issue Modelling of Nonlinear Dynamical Systems)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop