Related papers: Generic Torus Canards
The conventional approach to orbit trapping at Lindblad resonances via a pendulum equation fails when the parent of the trapped orbits is too circular. The problem is explained and resolved in the context of the Torus Mapper and a realistic…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
The R\"ossler System is characterized by a three-parameter family of quadratic 3D vector fields. There exist two one-parameter families of R\"ossler Systems exhibiting a zero-Hopf equilibrium. For R\"ossler Systems near to one of these…
The kinematic properties of unsteady highly non-linear 3D wave groups have been investigated using a numerical wave tank. Although carrier wave speeds based on zero-crossing analysis remain within +-7% of linear theory predictions, crests…
One of the most impressive features of moving animal groups is their ability to perform sudden coherent changes in travel direction. While this collective decision can be a response to an external perturbation, such as the presence of a…
Sparse Tucker Decomposition (STD) algorithms learn a core tensor and a group of factor matrices to obtain an optimal low-rank representation feature for the \underline{H}igh-\underline{O}rder, \underline{H}igh-\underline{D}imension, and…
We study the Tangled Nature model of macro evolution and demonstrate that the co-evolutionary dynamics produces an increasingly correlated core of well occupied types. At the same time the entire configuration of types becomes increasing…
Typicality of the orthogonal dynamics (TOD) is established as a generic feature of temporal relaxation processes in isolated many-body quantum systems. The basic idea in the simplest case is that the transient non-equilibrium behavior is…
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
Young stars form in molecular cores, which are dense condensations within molecular clouds. We have searched for molecular cores traced by $^{13}$CO $J=1\to 0$ emission in the Taurus molecular cloud and studied their properties. Our data…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
We report new dynamical modes in confined soft granular flows, such as stochastic jetting and dripping, with no counterpart in continuum viscous fluids. The new modes emerge as a result of the propagation of the chaotic behaviour of…
Flocking behavior is observed in biological systems from the cellular to super-organismal length scales, and the mechanisms and purposes of this behavior are objects of intense interest. In this paper, we study the collective dynamics of…
In this paper, we study ergodic properties of the slow relation function (or entry-exit function) in planar slow-fast systems. It is well known that zeros of the slow divergence integral associated with canard limit periodic sets give…
In the past fifteen years, flow instabilities reminiscent of the Taylor-like instabilities driven by hoop stresses, have been observed in wormlike micelles based on surfactant molecules. In particular, purely elastic instabilities and…
Mathematical models of reaction networks can exhibit very complex dynamics, including multistability, oscillations, and chaotic dynamics. On the other hand, under some additional assumptions on the network or on parameter values, these…
Dynamical systems with polynomial right-hand sides are very important in various applications, e.g., in biochemistry and population dynamics. The mathematical study of these dynamical systems is challenging due to the possibility of…
Knots and links are fundamental topological objects play a key role in both classical and quantum fluids. In this research, we propose a novel scheme to generate torus vortex knots and links through the reconnections of vortex rings…
We study a discrete-time asynchronous midpoint dynamics on the circle in which, at each step, a uniformly chosen neighboring pair moves to the midpoint along the shortest arc. Although the update rule is locally contractive, we show that…
An exponential horn geometry is introduced in order to establish cellular detonations with a constant mean lateral mass divergence, propagating at quasi-steady speeds below the Chapman-Jouguet value. Experiments and simulations demonstrated…