International Journal of Dynamical Systems and Differential Equations (4 papers in press)

Regular Issues

• Numerical Solution of Singular Autonomous Systems using the Fourth-Stage Geometric Mean Runge-Kutta Method  
  by Vijeyata Chauhan, Pankaj Kumar Srivastava 
  Abstract: The numerical treatment of singular problems is always seen to be intriguing, and its significance grows when it is raised in an autonomous system. This study proposes the development and implementation of a potent Runge-Kutta based fourth-stage explicit algorithm to numerically treat differential equations arising in the singular autonomous system. The basic properties of geometric mean have been brought into play to develop the algorithm. The convergence of the method has been established to prove the efficacy of the proposed technique. The consistency and stability of the method are also discussed. Two numerical illustrations are covered in the study and the results are compared with some other existing conventional methods, which confirms the importance of the method. The proposed method is found more efficient not only in terms of accuracy but also for applicability in first-order differential equations.
  Keywords: Explicit Runge-Kutta method; singular autonomous system; geometric mean; differential equations; increment function.
  DOI: 10.1504/IJDSDE.2025.10070393
   
  
• Modelling the Best Path Selection for Distributing Emergency Supplies in Earthquake Situations Using Ant Colony Optimisation Techniques  
  by Wenling Yu 
  Abstract: An optimal route selection model is proposed based on improved ant colony optimization (ACO) algorithm. Moreover, the effectiveness of the model is verified through simulation experiments. Firstly, the emergency materials distribution model of earthquake disasters, including route, starting, and ending points, is established to effectively evaluate the advantages and disadvantages of different routes. Secondly, the traditional ACO algorithm is enhanced by introducing new heuristic information, optimizing parameters, and increasing iterations to advance the convergence speed and accuracy of the algorithm and improve the shortcomings of the traditional ACO in its application. Finally, the simulation results show that the proposed algorithm and traditional ACO can calculate the optimal solution starting from node 0 after 27 cycles and 50 cycles. The experimental results reveal that the improved algorithm can find the optimal solution more quickly and has higher accuracy and stability.
  Keywords: Ant colony optimisation; algorithm; Earthquake disaster; Emergency material; Modelling; Optimal route.
  DOI: 10.1504/IJDSDE.2025.10071358
   
  
• Modeling Economic Cycle Fluctuations with Delayed Feedback Mechanisms: a Nonlinear AM-CNN-BiLSTM Approach  
  by Hong Zeng 
  Abstract: The real economy is subject to nonlinear influences such as consumer behaviour, enterprise investment dynamics, and delays in policy adjustments, all of which contribute to the complexity of economic system dynamics. To address the limitations of existing models, this study proposes a nonlinear framework incorporating delayed feedback mechanisms. Specifically, an AM-CNN-BiLSTM model is introduced, which integrates attention mechanisms, convolutional neural networks (CNNs), and bidirectional long short-term memory (BiLSTM) networks to capture sequential dependencies and enhance predictive accuracy. By simulating time-delay effects, the model effectively characterises the dynamic behaviour of economic systems. Experimental results demonstrate the presence of chaotic motion in the economic cycle system under certain parameter settings, as indicated by a maximum Lyapunov exponent of 0.1938. The proposed model exhibits strong predictive performance, achieving R2 = 0.9721, RMSE = 0.0552, and MAPE = 0.0235. These findings contribute to a deeper understanding of how delayed feedback mechanisms influence economic fluctuations and offer valuable insights for economic forecasting and policy formulation.
  Keywords: Nonlinear modelling; economic cycle fluctuations; delayed feedback mechanism; feature screening.
  DOI: 10.1504/IJDSDE.2025.10072006
   
  
• Topological Characterisation of 3D Digital Image Based on Topological and Betti Numbers  
  by Yibo Zhao 
  Abstract: The Euler-Poincare characteristic (EPC) is recognised as a key topological parameter in digital topology, commonly used to describe object connectivity and derive various quantities and functions. Its calculation is closely linked to Betti numbers, which represent the number of tunnels, cavities, and components. A new algorithm has been proposed for calculating the number of tunnels in a 3
  Keywords: Euler-Poincaré characteristics (EPCs); Topological numbers; Tunnels; Component.
  DOI: 10.1504/IJDSDE.2025.10072514