Weakly nonlinear analysis of a model of signal transduction pathway involving membrane based recptors

Rattanakul, Chontita; Lenbury, Yongwimon; Wollkind, David J.; Chatsudthipong, Varanuj

doi:10.1016/j.na.2009.02.005

Cited by 7 publications

(1 citation statement)

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“…In general, we will consider amplitude equations that have been discussed frequently in the context of pattern formation. The amplitude equations that will be presented below describe pattern formation in fluid layers under Benard instability [22,23,24,25,26,27,28,29,30], pattern formation in chemical reaction-diffusion systems [31], pattern formation in metal solidification processes [32] and the emergence of patterns in diffusive signaling processes in cells [33,34]. Moreover, the amplitude equations can be transformed into the form of Lotka-Volterra equations [35].…”

Section: Walking and Running Attractors: Definition Via Amplitude Equmentioning

confidence: 99%

Domains of attraction of walking and running attractors are context dependent: illustration for locomotion on tilted floors

Frank

2015

IJSW

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There is a general consensus that gaits of humans and animals can be considered as spatio-temporal patterns emerging via self-organization. In line with synergetics, a theory of pattern formation and self-organization founded by Haken, an amplitude equation model for human run-walk gait transitions is presented. The model allows for a definition of two distinct attractors representing walking and running. In particular, the size of the two attractors in the space of locomotion speed can be determined as a function of the model parameters. Furthermore, the model parameters can be estimated based on data from walking experiments on treadmills. The approach is illustrated for data reported in the literature on walking experiments involving tilted floors. It is shown that attractor size depends on the floor inclination, which suggests that in general the domains of attraction of walking and running attractors are context dependent. In particular, they depend on floor inclination. In other words, a pattern formation model is presented that describes how sensory feedback about environmental conditions may impact gait control.

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