| Citation: |
Seda Igret Araz. SEASONALITY OF RICKER MUTUALISM MODEL EMPLOYING RATE INDICATOR WITH ALMOST PERIODIC FUNCTION[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 312-327. doi: 10.11948/20250096
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SEASONALITY OF RICKER MUTUALISM MODEL EMPLOYING RATE INDICATOR WITH ALMOST PERIODIC FUNCTION
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Abstract
In this paper, we implement a rate indicator function featuring an almost periodic component to capture seasonal trends within the Ricker model, which represents a mutualistic framework. For the updated model incorporating this function, we derived parameters that guarantee the uniqueness of the solution and confirmed that the initial conditions do not affect the solution. We anticipate that this study will provide valuable insights into the critical role of the rate indicator function and the influence of almost periodicity in analyzing seasonal trends.
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Keywords:
- Almost periodicity /
- ecological model /
- seasonality /
- rate indicator
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References
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Seda Igret Araz. SEASONALITY OF RICKER MUTUALISM MODEL EMPLOYING RATE INDICATOR WITH ALMOST PERIODIC FUNCTION[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 312-327. doi: 10.11948/20250096
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Figure 1.
Graphical representation of the almost periodic function presented in Example 1.1.
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Figure 2.
Simulation showing the dynamics of the Ricker mutualism model in the absence of the almost periodic function.
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Figure 3.
Graphical representation of the dynamics of the function
$ P_{1}(t) $ -
Figure 4.
Graphical representation of the dynamics of the function
$ P_{2}(t) $ -
Figure 5.
Simulation of the function
$ P_{1}\left(t\right) $ -
Figure 6.
Simulation of the function
$ P_{2}\left(t\right) $ -
Figure 7.
Lyapunov exponents of Ricker's mutualism model with rate indicator function.
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Figure 8.
Graphical representation of each variable of the Ricker mutualism model with the rate indicator function over an extended time interval.
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Figure 9.
Phase plot of
$ P_{2}\left( t\right) $ $ P_{1}\left( t\right) $ -
Figure 10.
Bifurcation diagram of the Ricker mutualism model with the rate indicator function for varying values of
$ K_{1} $