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Revisiting the excess volatility puzzle through the lens of the Chiarella model. [PDF]
PLoS OneKurth JG, Majewski AA, Bouchaud JP.
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Global search metaheuristics for neural mass model calibration
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Zero‐Hopf bifurcation in the generalized Hiemenz equation
Mathematical Methods in the Applied Sciences, 2021In this work, we show the existence of zero‐Hopf periodic orbits in a 10‐parametric differential equation of third order where for . This family is based on a generalization of the equation associated to the Hiemenz flow, when the boundary conditions are neglected, and it will be named as generalized Hiemenz equation.
Marco Uribe, Elisa Martínez
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Analysis of Zero–Hopf Bifurcation in a Simple Jerk System
International Journal of Bifurcation and Chaos, 2023This work aims to study the zero–Hopf bifurcation of a jerk system with four real parameters. Some sufficient conditions of the emergence of periodic orbit and its stability at zero–Hopf equilibrium point are obtained by averaging theory.
Guo, Biyao +3 more
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A Generalist Predator and the Planar Zero-Hopf Bifurcation
International Journal of Bifurcation and Chaos, 2017A typical approach for searching periodic orbits of planar dynamical systems is through the Hopf bifurcation. In this work we present a family of predator–prey models with a generalist predator which does not exhibit a Hopf bifurcation, but a planar zero-Hopf bifurcation; that means, in the whole bifurcation process the eigenvalues of the linear ...
Valenzuela, Luis Miguel +2 more
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2014
In this chapter we study a bifurcation characterized by a zero eigenvalue and a pair of nonzero purely imaginary eigenvalues of the linearization transverse to a plane of equilibria. It turns out that instead we can study a one-parameter family of lines in a system depending on one parameter.
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In this chapter we study a bifurcation characterized by a zero eigenvalue and a pair of nonzero purely imaginary eigenvalues of the linearization transverse to a plane of equilibria. It turns out that instead we can study a one-parameter family of lines in a system depending on one parameter.
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Zero-Hopf bifurcation analysis on power system dynamic stability
2010 IEEE/PES Transmission and Distribution Conference and Exposition: Latin America (T&D-LA), 2010Under parametric variations, the phase portraits of a dynamical system such as a power system undergoes qualitative changes at bifurcation points. Several global codimension-two bifurcation points such as Zero-Hopf, generalized Hopf, Bogdanov-Takens, among others, can move the system much close to its instability limit, and lead to chaos.
S. Perez-Londono +2 more
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Hopf and Zero-Hopf Bifurcation Analysis for a Chaotic System
International Journal of Bifurcation and ChaosIn this paper, we investigate a quadratic chaotic system modeling self-excited and hidden attractors which is described by a system of three nonlinear ordinary differential equations with three real parameters. The primary goal is to establish the existence of two limit cycles that bifurcate based on the system’s nature as an electronic circuits model,
Ahmad Muhamad Husien, Azad Ibrahim Amen
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3-Dimensional zero–Hopf bifurcation via averaging theory of fourth order
São Paulo Journal of Mathematical SciencesThe authors study a three-dimensional ODE system defined by a cubic polynomial that exhibits a zero-Hopf bifurcation. They apply averaging theory and Brouwer degree to determine the maximum number of limit cycles that can emerge. Depending on the order of perturbation, the authors prove that at most 3 or 10 limit cycles can bifurcate. They also provide
Tabet, Achref Eddine +2 more
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Zero–Hopf bifurcations in Yu–Wang type systems
The European Physical Journal Special Topics, 2021Abimael Bengochea +2 more
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