arXiv subjects

Arhonefe Joseph Ogethakpo

Publications and source records attributed to Arhonefe Joseph Ogethakpo.

3 recordsLinked to original sources

arXiv2025

Analyzing Computational Approaches for Differential Equations: A Study of MATLAB, Mathematica, and Maple

Differential equations are fundamental to modeling dynamic systems in physics, engineering, biology, and economics. While analytical solutions are ideal, most real-world problems necessitate numerical approaches. This study conducts a detailed comparative analysis of three leading computational software packages: MATLAB, Mathematica, and Maple in solving various differential equations, including ordinary differential equations (ODEs), partial differential equations (PDEs), and systems of differential equations. The evaluation criteria include: Syntax and Usability (ease of implementation), Solution Accuracy (compared to analytical solutions), Computational Efficiency (execution time and resource usage), Visualization Capabilities (quality and flexibility of graphical outputs), Specialized Features (unique tools for specific problem types). Benchmark problems are solved across all three platforms, followed by a discussion on their respective strengths, weaknesses, and ideal use cases. The paper concludes with recommendations for selecting the most suitable software based on problem requirements

cs.MS↗

arXiv2025

The Lotka-Volterra Predator-Prey Model with Disturbance

The forces which drive growth, development, survival and change within an ecological system involving a predator and prey specie are not easily addressed in the field. To better understand the dynamics in the system, ecologists have turned to mathematical models. The predator-prey dynamics of rat and cat population in a given ecology is studied. The mathematical model proposed by Alfred J. Lotka and Vito Volterra called the Lotka-Volterra model for studying predator-prey dynamics is utilized. Assumptions were made to suit the given ecology. These assumptions lead to the modification of the Lotka-Volterra equations. The equilibrium and stability properties of the modified model is established. Results were simulated using MATLAB.

math.GM↗

arXiv2025

Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses

Urban ecosystems exhibit complex predator-prey dynamics increasingly disrupted by anthropogenic disturbances (e.g., noise, habitat fragmentation). Classical Lotka-Volterra (LV) models fail to capture these human-induced stressors, and integrated frameworks incorporating functional responses, stochasticity, and spatial dynamics remain scarce. We develop a comprehensive stochastic model to quantify how human disturbance reshapes predator-prey interactions in urban landscapes, using rat-cat systems as a case study. Our framework extends the LV model to incorporate: (i) human disturbance as an external mortality factor, (ii) Holling Type III functional responses to model predation saturation and prey refugia, (iii) multiplicative noise and periodic forcing to capture stochastic disturbance regimes, and (iv) spatial diffusion across fragmented habitats. We non-dimensionalize the system to generalize dynamics and analyze stability, bifurcations, and noise-induced transitions. Numerical simulations (MATLAB) reveal three key outcomes: (1) Human disturbance disrupts classical oscillations, inducing quasi-periodic cycles and elevating extinction risks; (2) Stochasticity lowers collapse thresholds by 25% compared to deterministic predictions; (3) Spatial diffusion drives pattern formation (e.g., disturbance shadows, prey hotspots) through habitat coupling. Results highlight the extreme vulnerability of urban wildlife to anthropogenic pressures, demonstrating how disturbance intensity governs system stability. The model provides a predictive framework for conservation strategies, emphasizing refuge enhancement and phased interventions synchronized with population cycles.

q-bio.PE↗