The route to chaos and the phase dynamics of the large scales in a rotating shallow-water model have been rigorously examined through the construction of an autonomous five-mode Galerkin truncated system employing complex variables, useful in investigating how large/meso-scales are destabilized and how their dynamics evolves and transits to chaos. This investigation revealed two distinct transitions into chaotic behaviour as the level of energy introduced into the system was incrementally increased. The initial transition manifests through a succession of bifurcations that adhere to the established Feigenbaum sequence.
View Article and Find Full Text PDFMuscle fatigue is the decay in the ability of muscles to generate force, and results from neural and metabolic perturbations. This article presents an integrative mathematical model that describes the decrease in maximal force capacity (i.e.
View Article and Find Full Text PDFBioengineering (Basel)
August 2022
Nonlinear dynamics have become a new perspective on model human movement variability; however, it is still a debate whether chaotic behavior is indeed possible to present during a rhythmic movement. This paper reports on the nonlinear dynamical behavior of coupled and synchronization models of a planar rhythmic arm movement. Two coupling schemes between a planar arm and an extended Duffing-Van der Pol (DVP) oscillator are investigated.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
August 2014
To study how nonlinear waves propagate across Y- and T-type junctions, we consider the two-dimensional (2D) sine-Gordon equation as a model and examine the crossing of kinks and breathers. Comparing energies for different geometries reveals that, for small widths, the angle of the fork plays no role. Motivated by this, we introduce a one-dimensional effective model whose solutions agree well with the 2D simulations for kink and breather solutions.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
June 2013
Extreme surface waves in a deep-water long-crested sea are often interpreted as a manifestation in the real world of the so-called breathing solitons of the focusing nonlinear Schrödinger equation. While the spontaneous emergence of such coherent structures from nonlinear wave dynamics was demonstrated to take place in fiber-optics systems, the same point remains far more controversial in the hydrodynamic case. With the aim to shed further light on this matter, the emergence of breatherlike coherent wave groups in a long-crested random sea is investigated here by means of high-resolution spectral simulations of the fully nonlinear two-dimensional Euler equations.
View Article and Find Full Text PDFThe estimation of the maximum wave run-up height is a problem of practical importance. Most of the analytical and numerical studies are limited to a constant slope plain shore and to the classical nonlinear shallow water equations. However, in nature the shore is characterized by some roughness.
View Article and Find Full Text PDFUntil now, the analysis of long wave run-up on a plane beach has been focused on finding its maximum value, failing to capture the existence of resonant regimes. One-dimensional numerical simulations in the framework of the nonlinear shallow water equations are used to investigate the boundary value problem for plane and nontrivial beaches. Monochromatic waves, as well as virtual wave-gage recordings from real tsunami simulations, are used as forcing conditions to the boundary value problem.
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