2021
DOI: 10.1186/s13662-021-03364-2
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Dynamics in a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays

Abstract: This study investigates the dynamical behavior of a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays. Compared with previous studies, both ratio-dependent functional responses and time delays are considered. By employing the comparison method, the Lyapunov function method, and useful inequality techniques, some sufficient conditions on the permanence, periodic solution, and global attractivity for the considered system are derived. Finally, a numerical… Show more

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Cited by 3 publications
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“…Figure 6 describes the flowchart of the DMOA algorithm: we initialize the parameters such as dimensions, epochs, number of iterations, etc., and we also initialize the two populations of plants and mycorrhizae; with these populations we find the best fitness of plants and mycorrhizae, while with these results we use the biological operators. The first operator is represented by the Lotka-Volterra System of Discrete Equations (LVSDE) Cooperative Model [ 62 ], whose result has inference on the other two models represented by LVSDE, Defense and Competitive [ 63 , 64 ], and in this frequency we evaluate the fitness to determine if it is better than the previous one and we update the same as the populations, if not we continue with the next iteration and continue the calculation with the biological operators. If the stop condition is fulfilled we obtain the last solution before evaluation and the algorithm ends.…”
Section: Discrete Mycorrhiza Optimization Algorithmmentioning
confidence: 99%
“…Figure 6 describes the flowchart of the DMOA algorithm: we initialize the parameters such as dimensions, epochs, number of iterations, etc., and we also initialize the two populations of plants and mycorrhizae; with these populations we find the best fitness of plants and mycorrhizae, while with these results we use the biological operators. The first operator is represented by the Lotka-Volterra System of Discrete Equations (LVSDE) Cooperative Model [ 62 ], whose result has inference on the other two models represented by LVSDE, Defense and Competitive [ 63 , 64 ], and in this frequency we evaluate the fitness to determine if it is better than the previous one and we update the same as the populations, if not we continue with the next iteration and continue the calculation with the biological operators. If the stop condition is fulfilled we obtain the last solution before evaluation and the algorithm ends.…”
Section: Discrete Mycorrhiza Optimization Algorithmmentioning
confidence: 99%