International Journal of Dynamical Systems and Differential Equations (5 papers in press)

Regular Issues

• The Information Perception Analysis of Complex Network based on Local Similar Clustering and BP Neural Network  
  by Meijing Song, Yajing Lu 
  Abstract: The social network’s development makes network public opinion (NPO) the most active expression of the public opinion in society, which can reflect the public opinion in cyberspace. NPO exerts more and more influence on the real society. It appears in the different stages of a variety of phenomena as well as issues in society, and has a significant impact on politics as well as public management in reality. How NPO evolves as well as the law of its evolution are studied in detail. Besides, a systematical analysis of the influence mechanism in its evolution is also made, which has crucial practical meaning. This exploration is based on a research angle that quite differs from previous studies, that is, the dynamic interactive network relationship among network members, government, media as well as Internet users.
  Keywords: Clustering; Complicated networks; Information public opinion; Local similarity.
  DOI: 10.1504/IJDSDE.2025.10072674
   
  
• Stochastic Modelling of Consumer Market Volatility an Improved Differential Equation Approach to Predicting Risk  
  by Xiang Chen 
  Abstract: In macroeconomic operations, consumption behaviour not only reflects the trends of economic variables such as residents income and market expectations, but also significantly influences policy regulation and industrial adjustment. In the context of increasing global uncertainty, traditional consumption forecasting methods demonstrate limited efficacy in modelling dynamic trajectories and structural fluctuations. This paper proposes a novel consumption fluctuation modelling approach, VAE-SDE, which integrates variational autoencoders (VAE) and stochastic differential equations (SDE). By extracting potential structural information from historical data through the VAE and mapping it to the SDE parameters, the method enables generative forecasting of consumption paths. This approach not only enhances the interpretability of the model but also improves its capacity for uncertainty modelling and path simulation.
  Keywords: Consumption forecasting; VAE; uncertainty modeling; SDE.
  DOI: 10.1504/IJDSDE.2025.10072739
   
  
• An Integrated Marketing Model based on Online Consumer Behaviour: a System Dynamics Stability and Classification Study  
  by Kan Lu, Mingting Huang 
  Abstract: In the complex realm of modern e-commerce, accurately modelling user interests and delivering personalised recommendations are essential for enhancing platform efficiency, user satisfaction, and business value. Traditional recommendation algorithms often struggle with key challenges such as capturing dynamic behavioural changes, effectively integrating multimodal features, and maintaining system stability during inference. To address these limitations, this study proposes the adaptive transformer and stability-enhanced network (ATRMST-Net). ATRMST-Net integrates a transformer-based sequential modelling backbone with a system dynamics-inspired stability control mechanism. A multimodal attention fusion module is designed to effectively aggregate heterogeneous user interaction data, enabling a richer understanding of user preferences. Furthermore, the model incorporates a temporal smoothness regularisation term and a Jacobian response control component to enhance robustness and mitigate the impact of noisy or volatile behaviours. Extensive experiments on multiple real-world e-commerce datasets demonstrate that ATRMST-Net consistently outperforms a range of competitive baselines across standard recommendation metrics. Ablation studies further confirm the individual contributions of each model component. Overall, this work provides a theoretically grounded and practically effective solution for building more stable, interpretable, and accurate recommendation systems in dynamic commercial environments.
  Keywords: personalised recommendation; multi-modal behaviour modelling; transformer with Stability Regularisation.
  DOI: 10.1504/IJDSDE.2025.10072888
   
  
• The Analysis of Wavelet Neural Networks for Urban Smart Transformation based on a Financially-Oriented Comprehensive Evaluation Model  
  by Jiaqian Liu, Tiantian Qu, Jiale Liu, Xiaojing Li 
  Abstract: This study proposes a financially-oriented comprehensive evaluation model to improve the accuracy and reliability of atmospheric pollution predictions during urban smart transformation. The model integrates wavelet transformation with Long Short-Term Memory (LSTM) networks and attention mechanisms to enhance predictive capabilities. Initially, data is decomposed and reconstructed using the Mallat algorithm from wavelet analysis. LSTM serves as the baseline prediction model, augmented with attention mechanisms and the Mallat algorithm to create a robust model for atmospheric pollution in smart transformation cities. Comparative evaluations against common neural network models, including LSTM, Bidirectional LSTM, Backpropagation Neural Networks, and wavelet neural networks, as well as LSTM with attention mechanisms, utilise average comparison error and the coefficient of determination to assess prediction results. This model enhances prediction accuracy and reliability while providing a scientific foundation for atmospheric pollution control and urban planning, contributing to sustainable urban development and environmental protection.
  Keywords: Urban smart transformation; Wavelet neural networks; Attention mechanism; Long Short-Term Memory Network; Mallat.
  DOI: 10.1504/IJDSDE.2025.10073142
   
  
• The Analysis of 3D Mathematical Space Design for Indoor Mapping based on Lumion Virtual Reality Simulation Technology  
  by Yihong Huang 
  Abstract: As space design becomes more intelligent and efficient, virtual simulation technology is continuously updated to provide designers with high-quality virtual reality (VR) landscape renderings. Based on market needs, an optimisation design method using Lumion plotting is proposed to enhance the simulation effect of virtual scene software. The process includes key steps such as data collection of the original scene, creation and import of the 3D model of the scene, preliminary rendering of the space model, placement of plants in the space scene, and optimisation of image details. The process utilises SketchUp software to create space models and import them into Lumion software. The results of four simulation design experiments in different scenarios show that the method used is a highly efficient VR space simulation design approach that requires less time and produces better visual results compared to the SketchUp for V-Ray and 3D Studio Max design methods.
  Keywords: Virtual Reality; Space Design; Anti-aliasing Design; Sampling; 3D Model; 3D Mathematical Space Design.
  DOI: 10.1504/IJDSDE.2025.10073176