Related papers: Ducks on the torus: existence and uniqueness
In this paper, we develop and analyze a model that studies the interaction between a specialist predator, a generalist predator, and their common prey in a two-trophic ecosystem featuring three timescales. We assume that the prey operates…
Given an ample line bundle on a toric surface, a question of Donaldson asks which simple closed curves can be vanishing cycles for nodal degenerations of smooth curves in the complete linear system. This paper provides a complete answer.…
We introduce a one-parameter family of polymatrix replicators defined in a three-dimensional cube and study its bifurcations. For a given interval of parameters, this family exhibits suspended horseshoes and persistent strange attractors.…
This article is the first in a series of two in which we study the vanishing cycles of curves in toric surfaces. We give a list of possible obstructions to contract vanishing cycles within a given complete linear system. Using tropical…
The idea that chaos could be a useful tool for analyze nonlinear systems considered in this paper and for the first time the two time scale property of singularly perturbed systems is analyzed on chaotic attractor. The general idea…
This paper studies a slow-fast system whose principal characteristic is that the slow manifold is given by the critical set of the cusp catastrophe. Our analysis consists of two main parts: first, we recall a formal normal form suitable for…
It is shown, under weak conditions, that the dynamical evolution of an important class of large systems of globally coupled, heterogeneous frequency, phase oscillators is, in an appropriate physical sense, time-asymptotically attracted…
We consider the planar Taylor-Couette system for the steady motion of a viscous incompressible fluid in the region between two concentric disks, the inner one being at rest and the outer one rotating with constant angular speed. We study…
We study fast-slow maps obtained by discretization of planar fast-slow systems in continuous time. We focus on describing the so-called delayed loss of stability induced by the slow passage through a singularity in fast-slow systems. This…
In this paper, we complete the global qualitative analysis of a quartic family of planar vector fields corresponding to a rational Holling-type dynamical system which models the dynamics of the populations of predators and their prey in a…
In this paper we analyse the phenomenon of the slow passage through a transcritical bifurcation with special emphasis in the maximal delay $z_d(\lambda,\varepsilon)$ as a function of the bifurcation parameter $\lambda$ and the singular…
Over the last few decades, complex oscillations of slow-fast systems have been a key area of research. In the theory of slow-fast systems, the location of singular Hopf bifurcation and maximal canard is determined by computing the first…
We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
This paper proposes a conceptual model for the onset of a stable torus near a saddle-focus equilibrium. This bifurcation scenario is typical of slow-fast systems that generate elliptic bursting in a variety of neuronal models in…
This work is motivated by a desire to understand transitions between stable equilibria observed in Stommel's 1961 thermohaline circulation model. We adapt the model, including a forcing parameter as a dynamic slow variable. The resulting…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
Kinematics and dynamics of a particle moving on a torus knot poses an interesting problem as a constrained system. In the first part of the paper we have derived the modified symplectic structure or Dirac brackets of the above model in…
This paper reports the finding of a simple one-parameter family of three-dimensional quadratic autonomous chaotic systems. By tuning the only parameter, this system can continuously generate a variety of cascading Lorenz-like attractors,…