International Journal of Dynamical Systems and Differential Equations (8 papers in press)

Regular Issues

• Sub-supersolutions method for singular quasilinear systems involving gradient terms  
  by Abdelkrim Moussaoui 
  Abstract: Existence, regularity and location of solutions to quasilinear singular elliptic systems with general gradient dependence are established developing a method of sub-supersolution. The abstract theorems involving sub-supersolutions are applied to prove the existence of positive solutions for convective and absorption singular systems
  Keywords: $p$-laplacian; singular systems; gradient estimate; regularity; convection; absorption; fixed point.
  DOI: 10.1504/IJDSDE.2026.10078837
   
  
• Dynamic analysis of an eco-epidemiological predator-prey model with fear and harvesting effects  
  by M. Varalaxmi, Md Golam Mortuja, Dipesh Dalal 
  Abstract: Model formation and the analysis of ecological systems are extremely important when using differential equations in population models. In this study, we propose and analyze a novel eco-epidemiological predator-prey model that integrates fear-induced behavioural responses, nonlinear predator harvesting, and disease transmission within the prey population. We establish the well-posedness of the system by proving positivity and boundedness of solutions. A complete qualitative analysis is carried out, including the existence and local stability of all biologically relevant equilibria. In particular, we derive explicit conditions under which predator harvesting induces a Hopf bifurcation. Numerical simulations are performed to validate the analytical findings. The results reveal that both excessive and insufficient harvesting can destabilise the system, potentially triggering population cycles or leading to extinction. Our findings provide new insights into how fear and harvesting jointly shape population dynamics and disease persistence, offering useful implications for ecological management.
  Keywords: Eco-epidemiology; Fear Effect; Harvesting; Stability; Hopf Bifurcation.
  DOI: 10.1504/IJDSDE.2026.10079959
   
  
• A new block Chebyshev-zero integrator for the numerical solution of second-order differential equations arising in classical mechanics  
  by Mark Modebei, Olumide Olaiya, Olugbade Faniyi 
  Abstract: Second-order initial value problems (IVPs) frequently arise in classical mechanics, where accurate and efficient numerical methods are essential for practical simulation. In this paper, we present a block linear multistep method formulated with hybrid points chosen as the zeros of Chebyshev polynomials of the first kind. The adoption of Chebyshev-based hybrid points enhances both the accuracy and stability of the scheme, thereby improving its efficiency compared with existing block methods. A detailed derivation of the method is provided, and its performance is assessed through a set of numerical experiments. The results indicate that the proposed method achieves higher accuracy while preserving computational efficiency, and compares favorably with other established techniques in the literature. The scheme is particularly applicable to problems in classical mechanics, including oscillatory systems and related second-order dynamical models.
  Keywords: Second-order initial value problems; Block linear multistep method; Hybrid points; Chebyshev zeros; Numerical simulation; Classical mechanics.
  DOI: 10.1504/IJDSDE.2026.10080943
   
  
• Optimal impulse Control and inverse problem of Degenerate Parabolic Equations with Robin Boundary Conditions  
  by Hind El Baggari, Ilham Ouelddris 
  Abstract: This paper addresses the time and norm optimal impulse control problems for one-dimensional degenerate parabolic equations subject to Robin boundary conditions, within the context of approximate impulse null controllability. To achieve this, we apply a logarithmic convexity estimate established in El Baggari and Ouelddris (2026), which yields an observation inequality for any set of positive measure. By overcoming the challenges of boundary degeneracy and weak impulsive actions, this framework enables a rigorous proof of the bang-bang property and the unique existence of optimal null controls. Furthermore, we explore the recovery of initial data from final-time observations, based on the principles of approximate impulse null controllability to reconstruct the initial data from the systems future state
  Keywords: Degenerate parabolic equations; Robin boundary conditions; impulsive systems; inverse problem; optimal control; approximate null controllability.
  DOI: 10.1504/IJDSDE.2026.10081223
   
  
• Dynamical Analysis of Predator-Prey Disease Model Incorporating Prey Refuge, Cannibalism, and Allee Effect  
  by Mohan Kumar G, Anupam Priyadarshi, Abhishek Kumar Singh 
  Abstract: We analyse a tri-trophic eco-epidemiological model with a prey population, a susceptible predator class, and an infected predator class, integrating a prey-refuge-modulated Holling Type II response, cannibalism in both predator compartments, a strong Allee effect, and saturating nonlinear disease incidence in a three-dimensional ODE framework. Positivity, boundedness, and five biologically feasible equilibria are established. Local stability is analysed via the Routh-Hurwitz criterion, and the basic reproduction number R0 is derived using the next-generation matrix method. Global stability of the prey-only and interior equilibria is proved using explicit Lyapunov methods. Bifurcation analysis reveals transcritical and Hopf bifurcations, with prey refuge governing transitions between stable coexistence and sustained oscillations. Sensitivity analysis identifies the disease transmission rate and saturation constant as key drivers of R0, while prey refuge and cannibalism dominate its reduction below threshold. Simulations confirm that prey refuge stabilises the system, cannibalism induces oscillations, and the Allee threshold governs predator persistence.
  Keywords: Allee effect; Cannibalism; Disease model; Prey refuge; Predator-prey dynamics.
  DOI: 10.1504/IJDSDE.2026.10081285
   
  
• A Milstein-Type Numerical Scheme for Clifford-Valued Stochastic Differential Equations  
  by Priya Nair, Mayavel P 
  Abstract: Stochastic differential equations with multivector-valued states arise naturally in geometric mechanics, rigid body dynamics, electromagnetism, and quantum systems. While first-order numerical schemes for Clifford-valued SDEs have recently been explored, no strong order-one methods currently exist. In this paper, we develop a Milstein-type discretization formulated directly in Clifford algebra coordinates, based on non-commutative stochastic Taylor expansions and Clifford differential calculus. The proposed method achieves strong convergence of order one under standard Lipschitz and linear growth conditions. We provide a rigorous convergence analysis, derive implementable algorithmic forms, and validate the scheme through numerical experiments on stochastic rotor dynamics. Superior accuracy and enhanced invariant preservation are shown in comparisons with the Euler--Maruyama schemes.
  Keywords: Clifford algebra; stochastic differential equations; Milstein method; convergence.
  DOI: 10.1504/IJDSDE.2026.10081326
   
  
• Qualitative Structures of Travelling Waves in a (3+1)-Dimensional Conformable Fractional Shallow Water Wave Equation  
  by M. Hemapriya, Adlin R. F. Rameesha, N. Keerthana, N. Annapoorani 
  Abstract: This study investigates exact traveling wave solutions of the (3+1)-dimensional conformable fractional shallow water wave equation using the modified Sardar sub-equation method. An appropriate traveling wave transformation reduces the governing fractional partial differential equation to an ordinary differential equation. The method constructs several classes of wave solutions, including solitary, periodic and rational forms. Phase portraits are presented to illustrate the qualitative structures and transitions across different parameter regimes, while three-dimensional surface plots and contour diagrams demonstrate the spatial and temporal evolution of the wave profiles. The primary contribution of this work is the derivation of a diverse set of new exact traveling wave solutions, supported by a comprehensive bifurcation analysis that reveals the underlying dynamical behavior and parameter dependent transitions. The results highlight the effectiveness of the proposed approach in capturing complex wave behavior in conformable fractional systems and provide useful insights for nonlinear wave theory and fluid dynamics.
  Keywords: Soliton theory; Exact solutions; Bifurcation theory; Fractional derivatives; Traveling wave solutions.
  DOI: 10.1504/IJDSDE.2026.10081729
   
  
• Design of Distributed Real-Time Control Unit Based on FreeRTOS and CAN Bus  
  by Guo Xin, Lei Gang, Shi Yun, Wang Tao 
  Abstract: A distributed real-time control unit based on FreeRTOS and CAN bus is developed to solve the problems of single-point failure, slow response and insufficient scalability in conventional centralized electrical control systems. Using the China-developed STC32G12K128 microcontroller as the core, it features modular hardware and a four-layer software architecture . Efficient measurement and control are realized through multi-task real-time scheduling and standard CANopen communication. Adopting a master-slave CAN bus network, the system forms a distributed control architecture for multi-node deployment, which avoids single-point failures and enhances scalability. Tested on an industrial robot flexible constant-force grinding platform, the control unit delivers an average response time of 8.2 ms and a maximum average relative error of 1.5% in pressure control. The CAN bus achieves a 99.9998% communication success rate over 72 hours, and the system runs stably for 30 days without hardware failures or downtime. The system outperforms traditional centralized schemes in real-time performance, control accuracy, communication reliability and stability, and is applicable to distributed measurement and control scenarios for industrial robots and engineering machinery.
  Keywords: FreeRTOS; CAN bus; CANopen protocol; STC32G12K128; distributed real-time control.