Results 11 to 20 of about 1,614 (256)
Darboux polynomials and global phase portraits for the D2 vector field [PDF]
Journal of Mathematical Analysis and Applications, 2019 We study a vector field of R^3 equivariant under the D_2 symmetry group, called "the D_2 field" in the literature. We construct the complete list of Darboux polynomials for it, solving the partial differential equation defining them. We also use these polynomials to comment on its global qualitative behaviour.
Katsios, Kostas, Anastassiou, Stavros
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Global phase portraits of the key pitchfork bifurcation [PDF]
SCIENTIA SINICA Mathematica, 2019 This paper deals with the following quadratic polynomial differential system$\frac{dx}{dt}=y^{2}-y-x,$ $\frac{dy}{dt}=x^{2}$ $-\,~\mu~x-y,$with parameter $\mu\in\mathbb{R}$, which is the key example for studying the pitchfork bifurcation of a singular point. We classify the global phase portraits in the Poincare disc of this system when $\mu$ varies.
Jaume, Llibre, Shimin, Li
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Global phase portraits of the generalized van der Pol systems
Bulletin des Sciences Mathématiques, 2023 We consider the generalized van der Pol systems x˙ = y, y˙ = -x + (1-x) f(y), where f ∈ R[y]. The classical van der Pol systems have f(y) = y. We first characterize when the origin of the generalized van der Pol systems is a center, and second we provide the global phase portraits in the Poincaré disc of the generalized van der Pol when f(y) = ay + ay ...
Jaume Llibre, Claudia Valls
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Dynamical Behaviour, Control, and Boundedness of a Fractional-Order Chaotic System
Fractal and Fractional, 2023 In this paper, the fractional-order chaotic system form of a four-dimensional system with cross-product nonlinearities is introduced. The stability of the equilibrium points of the system and then the feedback control design to achieve this goal have ...
Lei Ren +3 more
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Frontiers in Applied Mathematics and Statistics, 2023 The complexity of the dynamical behaviors of interaction between prey and its predator is studied. The prey and predator relationship involves the age structure and intraspecific competition on predators and the nonlinear harvesting of prey following the
Hasan S. Panigoro +2 more
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Risks assessment and forecasting long time rows of economic indicators [PDF]
Экономика региона, 2012 This paper reviews main approaches to risk assessment. The authors accented attention on the nonlinear approach to the theory of risks. It is proposed to define economic risk as the probability of threats that could have material adverse effect on the ...
Gennadiy Pavlovich Bystray +2 more
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Dynamical Behaviors in a Stage-Structured Model with a Birth Pulse
Mathematics, 2023 This paper presents an exploitation model with a stage structure to analyze the dynamics of a fish population, where periodic birth pulse and pulse fishing occur at different fixed time.
Yun Liu, Lifeng Guo, Xijuan Liu
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Bifurcation Diagrams and Global Phase Portraits for Some Hamiltonian Systems with Rational Potentials [PDF]
International Journal of Bifurcation and Chaos, 2018 In this paper, we study the global dynamical behavior of the Hamiltonian system [Formula: see text], [Formula: see text] with the rational potential Hamiltonian [Formula: see text], where [Formula: see text] and [Formula: see text] are polynomials of degree 1 or 2.
Ting Chen, Jaume Llibre
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GLOBAL PHASE PORTRAITS OF SOME REVERSIBLE CUBIC CENTERS WITH COLLINEAR OR INFINITELY MANY SINGULARITIES [PDF]
International Journal of Bifurcation and Chaos, 2012 We study the reversible cubic vector fields of the form ẋ = -y + ax2+ bxy + cy2- y(x2+ y2), ẏ = x + dx2+ exy + fy2+ x(x2+ y2), having simultaneously a center at infinity and at the origin. In this paper, the subclass of these reversible systems having collinear or infinitely many singularities are classified with respect to topological equivalence.
Caubergh, M., Llibre, J., Torregrosa, J.
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Global Analysis of a Liénard System with Quadratic Damping
Discrete Dynamics in Nature and Society, 2018 In this paper, the global analysis of a Liénard equation with quadratic damping is studied. There are 22 different global phase portraits in the Poincaré disc.
Feng Guo
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