Page 2 - POSTER FYP MAC-OGOS 2025

DYNAMICAL ANALYSIS OF PREY-PREDATOR SYSTEM
WITH THE EFFECT PREDATOR GROWTH RATE USING
SUPERVISOR: MADAM ZATI IWANI ABDUL MANAF
FACULTY OF COMPUTER AND MATHEMATICAL SCIENCES, UITM CAWANGAN KELANTAN KAMPUS MACHANG
ABSTRACT
Predator-prey models are widely used in ecological modeling
to explain population dynamics. However, many existing
models assume a constant predator growth rate, which may
not reflect real-world ecological conditions. Therefore, this
project focuses on the influence of variable predator growth
rates of a prey-predator system to address the limitations of
such existing models. A modified Lotka-Volterra model was
developed by incorporating intraspecific prey competition and
a dynamic predator growth rate to more accurately represent
ecological interactions. To analyze the proposed model, a
combination of symbolic and numerical tools was employed.
Specifically, Maple was used for symbolic computations,
including the computation of equilibrium points, Jacobian
matrices, and eigenvalues for local stability analysis.
Meanwhile, XPPAUT supported numerical integration and the
construction of one-parameter bifurcation diagrams to detect
critical transitions such as transcritical bifurcations. In
addition, MATLAB was utilized to generate phase plane plots
and time series graphs, which provided visual insight into the
system’s dynamic responses. The results indicate that changes
in the predator growth rate can significantly influence system
stability, potentially leading to population oscillations or
extinction scenarios. As a result, incorporating realistic
predator growth mechanisms enhances the predictive power of
ecological models. Ultimately, these improvements contribute
to better ecosystem management, biodiversity conservation,
and ecological forecasting.
METHODOLOGY
Phase 1: Formulating Mathematical Model
Equation from Mustapha and Nazrri
(2023)
Phase 2: Stability Analysis
Determine the equlibrium point
Let
Calculate Jacobian Matrix
Let
Then,
Calculate eigenvalues by letting:
Let
Equilibrium point classification
According to the type and sign of
Phase plane for each critical point category
Phase 3: Bifurcation Analysis
The parameter value
Plot bifurcation diagram to capture B point,
slicing bifurcation diagram before/after B
Plot phase plane and time series diagram
ONE-PARAMETER BIFURCATION
NAME: FATIN NATASYA BINTI ZAINUDDIN K242/02
PROBLEM STATEMENT OBJECTIVE
Conventional predator-prey models, such as the classical To fomulate the prey-predator model with growth
Lotka-Volterra system, often assume a constant growth rate of predator.
rate for the predator population. This simplification fails To analyze the stability analysis of the prey-
to capture the dynamic nature of real ecosystems, where predator model with growth rate of predator.
predator growth is influenced by factors like food To analyze the impact of the predator growth rate
availability, environmental changes, and biological using one-parameter bifurcation analysis
conditions. As a result, such models may not accurately
reflect how predator and prey populations interact over
time. This study addresses this gap by proposing a model
that incorporates a variable predator growth rate, Result and Discussion
aiming to provide a more realistic and adaptable
framework. Through stability and bifurcation analysis,
the research seeks to identify how changes in predator Summary of stability and bifurcation analysis with respect to
level of predator growth rate, m
growth can shift ecosystem dynamics, offering insights
that could improve ecological predictions and
conservation strategies.
Implementation
Jacobian matrix for
One-parameter bifurcation
Jacobian matrix for
The slicing of one-parameter bifurcation
diagram
Modified equation
Jacobian matrix for
Phase plane diagram
Growth rate of predator , m = 0.525
Growth rate of predator , m = 0.535
Conclusion
This study offers a more realistic approach to modeling predator-prey
dynamics through the introduction of a variable predator growth rate
—a key element often overlooked in traditional models. Through
stability and bifurcation analysis, the research highlights how small
and changes in this growth rate can radically shift the balance between
species, driving them toward extinction or coexistence.
It is essential for ecologists, conservation planners, and policymakers
to be aware of these dynamics because it guides them in making
Time series diagram
informed decisions on biodiversity conservation, species management,
and ecological prediction. By providing a model that better reflects
Growth rate of predator , m = 0.525
population behavior in the real world, this study not only propels
mathematical ecology forward but also informs real-world efforts to
preserve ecosystem stability in the face of environmental change.
Recommendation
To make the findings more generalizable and reliable, some
suggestions for future research are made. First, employing
actual ecological data in the model would make it far more
accurate and useful. By doing a test run of the model using Growth rate of predator , m = 0.535
empirical data from actual predator-prey systems, the results
can be used more effectively to guide environmental policy and
conservation initiatives.
Finally, driving the use of computation software like MATLAB,
Maple, and XPPAUT will again generate more precise
simulations and simpler visualizations. Improved graphics and
analytic analysis will benefit researchers and policymakers to
grasp results more effectively and apply them to ecosystem
management.