On the critical periods of Liénard systems with cubic restoring forces
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 61, Page 3259-3274, 2004., 2004 We study local bifurcations of critical periods in the neighborhood of a nondegenerate center of a Liénard system of the form x˙=−y+F(x), y˙=g(x), where F(x) and g(x) are polynomials such that deg(g(x)) ≤ 3, g(0) = 0, and g′(0) = 1, F(0) = F′(0) = 0 and the system always has a center at (0, 0). The set of coefficients of F(x) and g(x) is split into two
Zhengdong Du
wiley +1 more source
Open Mathematics, 2019 In this paper, we show the existence of an S-shaped connected component in the set of radial positive solutions of boundary value ...
Xu Man, Ma Ruyun
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Hopf bifurcations in a three-species food chain system with multiple delays
Open Mathematics, 2017 This paper is concerned with a three-species Lotka-Volterra food chain system with multiple delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the stability of the positive equilibrium and ...
Xie Xiaoliang, Zhang Wen
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Some results on homoclinic and heteroclinic connections in planar systems [PDF]
, 2009 Consider a family of planar systems depending on two parameters $(n,b)$ and having at most one limit cycle. Assume that the limit cycle disappears at some homoclinic (or heteroclinic) connection when $\Phi(n,b)=0.$ We present a method that allows to ...
Andronov A A +12 more
core +4 more sources
Complex dynamics of a predator–prey model with opportunistic predator and weak Allee effect in prey
Journal of Biological Dynamics, 2023 In this work, we first modify a Lotka–Volterra predator–prey system to incorporate an opportunistic predator and weak Allee effect in prey. The prey will be extinct if the combined effect of hunting and other food resources of predator is large ...
Zhenliang Zhu +3 more
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Global periodic solutions in a plankton-fish interaction model with toxication delay
Nonlinear Engineering, 2018 In this paper, a plankton-fish interaction model is proposed and analyzed with the help of delay differential equations. Firstly, the elementary dynamical properties of the system in the absence of time delay is discussed.
Sharma Amit
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The jump phenomenon associated with the dynamics of the duffing equation
Physics Open, 2020 The mathematical nature of the jump phenomenon associated with the damped, harmonically forced Duffing equation is investigated, as regards the amplitude of the harmonic response of the system.
M.P. Markakis
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A Comparison of the Trojan Y Chromosome Strategy to Harvesting Models for Eradication of Non-Native Species [PDF]
, 2019 The Trojan Y Chromosome Strategy (TYC) is a promising eradication method for biological control of non-native species. The strategy works by manipulating the sex ratio of a population through the introduction of \textit{supermales} that guarantee male ...
Hill J. E. +5 more
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The spin-orbit resonances of the Solar system: A mathematical treatment matching physical data
, 2013 In the mathematical framework of a restricted, slightly dissipative spin-orbit model, we prove the existence of periodic orbits for astronomical parameter values corresponding to all satellites of the Solar system observed in exact spin-orbit ...
Antognini, Francesco +2 more
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Chaos and bifurcation in the controlled chaotic system
Open Mathematics, 2018 In this paper, chaos and bifurcation are explored for the controlled chaotic system, which is put forward based on the hybrid strategy in an unusual chaotic system.
Liu Yongjian +2 more
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