| Citation: |
Xin Yang, Yongping Zhang, Yuan Jiang. CONTROL AND SYNCHRONIZATION OF FRACTAL BEHAVIORS OF THE DISCRETE FRACTIONAL T-S FUZZY PREY-PREDATOR MODEL[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 1054-1073. doi: 10.11948/20250090
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CONTROL AND SYNCHRONIZATION OF FRACTAL BEHAVIORS OF THE DISCRETE FRACTIONAL T-S FUZZY PREY-PREDATOR MODEL
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Abstract
There are important significances to discuss the prey-predator model in various aspects such as biodiversity conservation, resource management, ecosystem services and so on. At first, to investigate the fractal behavior of the predator-prey model from a fractal perspective, the two-dimensional continuous prey-predator model is discretized, and its Caputo fractional-order form is obtained. Secondly, utilizing the sector nonlinear method, a Takagi-Sugeno (T-S) fuzzy model of the discrete fractional-order predator-prey model is established, and the Julia set of the model based on the T-S fuzzy model is introduced. Thirdly, a parallel distributed compensation (PDC) approach is employed to design the corresponding fuzzy controller, and sufficient conditions for the stability of the system are given in the form of linear matrix inequalities (LMIs). The controller gain parameters are obtained by solving LMIs, and control of the Julia set of the discrete fractional-order predator-prey model based on the T-S fuzzy model is carried out. Finally, using the exact linearization technique, synchronization of the Julia sets of the predator-prey models is achieved based on the T-S fuzzy model by the linear control method.
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Keywords:
- Prey-predator model /
- T-S fuzzy model /
- Julia set /
- synchronization
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References
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Xin Yang, Yongping Zhang, Yuan Jiang. CONTROL AND SYNCHRONIZATION OF FRACTAL BEHAVIORS OF THE DISCRETE FRACTIONAL T-S FUZZY PREY-PREDATOR MODEL[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 1054-1073. doi: 10.11948/20250090
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Figure 1.
Julia sets of system (3.7) when the parameters are taken as
$ \varepsilon_{1}=0.2, \ \gamma_{1}=0.15, \ \varepsilon_{2}=0.1, \ \gamma_{2}=0.1 $ -
Figure 2.
Julia set of model (4.2) when
$ \varepsilon_{1}=0.2, \ \gamma_{1}=0.15, \ \varepsilon_{2}=0.1, \ \gamma_{2}=0.1, \ \mu=0.9 $ -
Figure 3.
Julia sets of system (4.2) with varying controller parameters, when the parameters are taken as
$ \varepsilon_{1}=0.2, \ \gamma_{1}=0.15, \ \varepsilon_{2}=0.1, \ \gamma_{2}=0.1 $ $ \mu $ -
Figure 4.
Julia set of model (3.7) when
$ \varepsilon_{1}=0.2, \ \gamma_{1}=0.15, \ \varepsilon_{2}=0.1, \ \gamma_{2}=0.1, \ \mu=0.9 $ -
Figure 5.
Julia set of model (3.7) when
$ \varepsilon_{3}=0.01, \ \gamma_{3}=0.2, \ \varepsilon_{4}=1, \ \gamma_{4}=0.3, \ \mu=0.9 $ -
Figure 6.
Synchronization of Julia set of model (3.7) by changing the coefficients of
$ W $ $ Z $ $ \varepsilon_{1}=0.2, \ \gamma_{1}=0.15, \ \varepsilon_{2}=0.1, \ \gamma_{2}=0.1, \ \varepsilon_{3}=0.01, \ \gamma_{3}=0.2, \ \varepsilon_{4}=1, \ \gamma_{4}=0.3, \ \mu=0.9 $