Page 3 - POSTER FYP MAC-OGOS 2025

01 ABSTRACT
FACULTY OF COMPUTER AND MATHEMATICAL SCIENCES, UITM CAWANGAN
KELANTAN KAMPUS MACHANG
K242/03
In this study, the effect of predator death rate on prey-predator dynamics was investigated using a modified Lotka-
THE INFLUENCE OF PREDATOR Volterra model. Existing ecological models often overlooked the role of predator death rate, which was also critical for

DEATH RATE ON PREY- ecological balance. Therefore, this project aimed to examine how variations in predator death rate affect system
PREDATOR MODEL USING stability and species coexistence. To analyze the system behavior, XPPAUT software was employed to one-parameter
bifurcation analysis, while stability analysis was conducted using MAPLE. Additionally, phase plane and time series
ONE-PARAMETER simulations were plotted using MATLAB. The results showed that predator death rate significantly influenced system
BIFURCATION ANALYSIS behavior. A transcritical bifurcation point was identified at d=0.42, signaling a change from stable co-existence to
predator extinction. For instance, both species coexisted at d=0.40. However, when the death rate increased at d=0.44,
predators went extinct and prey dominated. In conclusion, these findings underscore the ecological importance of
NAME: NORSAFIAH BINTI ISMAIL
SUPERVISOR: MADAM ZATI IWANI BINTI ABDUL MANAF maintaining balanced predator death rates in order to ensure long-term ecosystem.

02 PROBLEM STATEMENT 04 METHODOLOGY

Existing ecological models often emphasize predator growth based on prey PHASE 1: FORMULATING MATHEMATICAL MODEL
availability but overlook the complex factors contributing to predator mortality PHASE 3: 0NE-PARAMETER BIFURCATION ANALYSIS
Original formula from New model The parameter values used in prey-predator system
such as disease, environmental stress, and human interference. These factors
Zhu et al. (2020)
play a crucial role in shaping population dynamics and ecosystem stability.
Although recent models, like the one by Zhu et al. (2020), introduced the fear
effect and alternative food sources, they still underrepresent the predator's
death rate as a dynamic variable. This study aims to address that gap by
analyzing how changes in predator mortality influence prey-predator 1.Plot bifurcation diagram to capture bifurcation
interactions. Using a modified Lotka-Volterra model and one-parameter PHASE 2: STABILITY ANALYSIS 3.Calculate the eigenvalues point (B)
bifurcation analysis, the research seeks to offer a more realistic and 1.Determine the equilibrium point Let
comprehensive understanding of ecological balance for better ecosystem Let
management. Then,
2. Slicing bifurcation diagram before and after the
2. Calculate the Jacobian Matrix bifurcation point (B)
Let
; 4. Determine eigenvalues
03 OBJECTIVES Based on the sign and nature
Then, of and
3. Plot phase plane and time series
Phase plane for each
1.To formulate a prey-predator model with death rate in predator
equilibrium points
2.To perform the stability analysis of the formulated model by determining
equilibrium points and its classification After that,
3.To investigate the impact of predator death rate on prey-predator
dynamics using one-parameter bifurcation analysis

05 IMPLEMENTATION 06 RESULTS AND DISCUSSIONS

EQUILIBRIUM POINTS 2. One-parameter bifurcation diagram for (x,y)
1.Numerical analysis results when d was varied toward death rate of predator 3. Slicing of one-parameter bifurcation diagram

ANALYSIS OF LOCAL STABILITY FOR E
1

Jacobian Matrix for E 1
4. 2D phase portrait for prey-predator populations
5. Time series graph for prey-predator
Eigenvalues for E 1
;
ANALYSIS OF LOCAL STABILITY FOR E
2

The blue solid line represented the prey
population that increased quickly at first
Jacobian Matrix for E 2
before stabilizing at a high-steady state value
near 0.7.
On the other hand, the predator population,
which was the red dashed line, decreased
drastically over time in figure 5.(a)
Eigenvalues for E 2
; The system demonstrated a coexistence steady stable
state at equilibrium, where both prey and predator
populations existed in figure 4.(a)
ANALYSIS OF LOCAL STABILITY FOR E
3

The blue solid line represented the prey
Jacobian Matrix for E 3 population, which started at a low value (0.1)
and increased significantly before stabilizing
at its maximum normalized value of 1.
In contrast, the red dashed line showed the
M > 0 is equal to predator population, which began at 0.4 but
rapidly declined to zero early in the
simulation and remained extinct thereafter in
figure 5.(b)
N > 0 is equal to
The direction field and trajectories from different initial
conditions moved toward the equilibrium point E2 = (1, 0),
which indicated that E2 was an asymptotically stable node
in figure 4.(b)

07 CONCLUSION 08 RECOMENDATION 09 REFERENCES

All three objectives have been achieved Future research should consider expanding the model to include additional 1.Zhu, Z., Wu, R., Lai, L., & Yu, X. (2020).
Predator death rate significantly impacts system equilibrium and long-term behavior. ecological factors and spatial dynamic The influence of fear effect to the
A transcritical bifurcation at d = 0.42 marked a critical behavioral shift. Explore other bifurcations (e.g., Hopf) to detect oscillatory behaviors. Lotka-Volterra predator-prey system
with predator has other food resource.
Predator death rate is crucial for maintaining ecological balance. Validate the model with real-world data to enhance its practical application
Advances in Difference Equations,
Demonstrates how small ecological changes can lead to major population shifts. in ecological management. 2020, 1–13.