A problem of stability of parametrical system of two coupled circuits with external conductive connection

Biryuk, N. D.; Nechaev, Yu. B.; Alyohin, S. Yu.

doi:10.3103/s0735272708080049

Cited by 3 publications

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“…As in Theorem 1, the boundedness analysis of the state parameters (𝒚 𝟏 , 𝒚 𝟐 ) , describing the system (1) depends on the scalar differentiable Lyapunov function 𝑽(𝒚 𝟏 , 𝒚 𝟐 ) defined in (3). Here, we consider the heterogenous case where 𝝀𝑮(𝒚 𝟏 ) ≠ 𝟎 and 𝝁𝑭(𝒚 𝟐 ) ≠ 𝟎 in (1).…”

Section: Boundedness Analysismentioning

confidence: 99%

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Stability and Boundedness Analysis of Lotka-Volterra Prey-Predator Model with Prey Refuge and Predator Cannibalism

OLUTIMO¹,

AKINMOLADUN²,

OMOKO³

2022

Journal of Computations &Amp; Modelling

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In this paper, a prey-predator system incorporating prey refuge and predator cannibalism is studied. The stability and ultimate boundedness of the analyzed state parameters (y_1,y_2) defining the system are obtained using the Lyapunov’s second or direct method. We construct a suitable complete Lyapunov function for the nonlinear system and demonstrate its efficacy. The method is built upon applying various theoretical Lyapunov functions. By constructing a Lyapunov function which possesses a functional relationship to the the original model system, we give sufficient conditions which ensure the stability and ultimate boundedness of the state parameters describing the nonlinear prey-predator system. We give a numeric example to illustrate the result obtained. JEL classification numbers: 34C27, 34D23, 34C25. Keywords: Prey-predator system, Prey refuge, Predator cannibalism, Stability, Boundedness, Lyapunov’s method.

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Section: Boundedness Analysismentioning

confidence: 99%

“…Lyapunov functional approach remains an excellent tool in the study of dynamical systems. see (Qin, et al 1966), (Biryuk, et al 2008), (Olutimo and Omoko, 2020). However, the construction of these Lyapunov functional is indeed a general problem.…”

Section: Introductionmentioning

confidence: 99%