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- Title
Nonlinear Model for Aphid and Ladybugs Interaction with Pesticides as Fuzzy Parameters.
- Authors
Noviantri, Viska; Alexander, Kelvin; Suandi, Dani; Achmad, Said; Br Sipahutar, Angel Marcelina
- Abstract
Pesticides are the most common method used to eliminate pests, including aphids. Pesticides are the most common method used to eliminate pests, including aphids. Nonetheless, numerous farmers incorporate ladybugs into their pest management strategies as they serve as natural predators of aphids. By integrating these methods, farmers aim to achieve optimal outcomes in mitigating the detrimental effects of aphids on the agricultural sector. In this paper, the dynamics of interactions between aphids and ladybugs, including the impact of pesticides on aphid mortality, are represented using a system of nonlinear differential equations. This study treats the parameter representing aphid mortality caused by pesticides as a fuzzy number to account for variations in resistance levels. Additionally, the model incorporates four parameters that depict the interaction between aphids and ladybugs beyond considering the effect of pesticides. The parameters include the proportion of aphids consumed by ladybugs, the proportion of aphids capable of evading ladybugs, and the growth rates of both aphids and ladybugs. The triangular form is chosen to depict the fuzzy membership function because it reflects the resistance of aphids when pesticides are applied excessively. The dynamic model, incorporating a fuzzy parameter, is transformed into discrete-time models using the Non-Standard Finite Difference (NSFD) method for simulation purposes. The simulation outcomes align with the analysis findings, indicating a potential equilibrium between the populations of aphids and ladybugs. Various examinations on the impact of fuzzy pesticide parameters on the growth of aphids and ladybugs are provided. The findings demonstrate that pesticide application can substantially decrease the aphid population and can be tailored based on the interplay between aphids and ladybugs. Moreover, pesticide usage can be diminished with heightened ladybug growth and predation rates, thereby minimizing the occurrence of resistant aphids and enhancing the effectiveness of pesticide application.
- Subjects
APHIDS; LADYBUGS; NONLINEAR differential equations; NONLINEAR equations; PESTICIDES; FINITE differences; PEST control; MEMBERSHIP functions (Fuzzy logic)
- Publication
IAENG International Journal of Applied Mathematics, 2024, Vol 54, Issue 6, p1182
- ISSN
1992-9978
- Publication type
Article