arXiv subjects

Pedro Iván Suárez Navarro

Publications and source records attributed to Pedro Iván Suárez Navarro.

5 recordsLinked to original sources

arXiv2026

Zero-Hopf Bifurcation of Qi hyperchaotic Systems

In this paper, we show a zero-Hopf bifurcations in a four-dimensional hyperchaotic Qi system. While the hyperchaotic dynamics of this model have been extensively investigated, the existence and bifurcation of zero-Hopf equilibria have not been previously analyzed. We first characterize the equilibrium points and determine the parameter conditions under which the origin becomes a zero-Hopf equilibrium. Using second-order averaging theory, we establish the existence of up to four small amplitude periodic solutions bifurcating from the origin under suitable parameter perturbations. We also provide analytical expressions for the initial conditions of these solutions.

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arXiv2026

Crossing limit cycles of discontinuous piecewise differential systems with nilpotent saddles separated by a nonregular line

In this paper, we study crossing limit cycles of planar discontinuous piecewise differential systems separated by a nonregular switching line, where one subsystem is a linear differential center and the other belongs to one of six families of Hamiltonian nilpotent saddle systems. This work extends previous results for discontinuous piecewise differential systems separated by a straight line to the more general setting of nonregular switching boundaries. The problem is closely related to the second part of Hilbert's 16th problem for discontinuous piecewise differential systems. We prove that the systems under consideration admit at most seven crossing limit cycles. Moreover, for each family of Hamiltonian nilpotent saddle systems, we provide explicit examples exhibiting four crossing limit cycles.

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arXiv2026

Crossing limit cycles of discontinuous piecewise differential systems with Pleshkan's isochronous centers

In recent decades, piecewise linear differential systems have attracted considerable attention due to their ability to describe a wide range of phenomena. A central problem, as in the theory of general planar differential systems, is to determine the existence and the maximal number of crossing limit cycles. However, deriving sharp upper bounds for this quantity remains a highly challenging problem. In this work we study crossing limit cycles in planar discontinuous piecewise differential systems separated by a straight line, where each subsystem is either a linear center or a cubic isochronous center with homogeneous nonlinearities. Within this setting, we consider all possible combinations arising from these families, leading to fifteen distinct classes of piecewise systems. Using the existence of first integrals, we reduce the detection of crossing limit cycles to algebraic closing conditions on the discontinuity set, which allows for a systematic and unified analysis across all configurations. As a consequence, we establish explicit upper bounds for the number of crossing limit cycles in all cases except for three configurations that remain open. In addition, we construct examples exhibiting three crossing limit cycles in every class, providing a nontrivial uniform lower bound. Our results extend and complement earlier work in the literature by including previously unstudied configurations and improving some known bounds, thereby providing a comprehensive description of the number of crossing limit cycles within this class of systems

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arXiv2026

Emergence of Mandelbrot-like and Julia-like Structures in Parameter Slices of Rational Maps

We study complex one-dimensional parameter slices in a three-parameter family of rational maps with two free critical points, obtained by imposing the existence of periodic orbits with prescribed multipliers. Using explicit parametrizations, we explore these slices numerically by analyzing the behavior of the critical orbits and approximating the corresponding connectedness loci. The computations reveal rich parameter space structures closely analogous to those arising in cubic polynomial families, including Mandelbrot-like sets. In addition, we observe regions exhibiting Julia-like structures embedded in parameter space, arising from the interaction between bounded and escaping critical orbits. While the appearance of such structures is well established in polynomial dynamics, it remains comparatively less explored in the setting of rational maps. Our results provide numerical evidence that these parameter slices contain subsets closely related to the period-one and period-two slices of cubic polynomial families. More precisely, certain regions appear to exhibit geometric and dynamical features consistent with embedded copies of these classical parameter spaces. These observations highlight how classical structures from polynomial dynamics can emerge naturally within parameter slices of rational maps.

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arXiv2026

Emergence of Multiple Crossing Limit Cycles in Planar Piecewise Systems with Isochronous Centers and Nonsmooth Switching Manifolds

Discontinuous piecewise differential systems exhibit dynamical behaviors with no counterpart in smooth systems, particularly in the presence of nonsmooth switching structures. In this work, we extend previous results for systems separated by a straight line to the case where the switching manifold is a nonregular curve, showing that the loss of regularity significantly increases the algebraic complexity of the closing conditions defining crossing limit cycles. As a consequence, we derive explicit upper bounds for the number of crossing limit cycles in planar systems formed by a linear Hamiltonian saddle and quadratic isochronous centers, and construct explicit examples exhibiting four crossing limit cycles in each case, thereby providing sharp constructive lower bounds. While the upper bounds follow from classical algebraic arguments, the realization of multiple crossing limit cycles requires solving nonlinear systems of high degree and remains highly nontrivial. These results highlight how nonsmooth switching manifolds enhance dynamical complexity and promote multistability in discontinuous piecewise systems

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