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Fig. 8 | The Journal of Mathematical Neuroscience

Fig. 8

From: Phase-Amplitude Descriptions of Neural Oscillator Models

Fig. 8

Stretch-and-fold action of a kick followed by relaxation in the presence of shear. The thin black lines are the isochrons of the system, which in the case of the linear model (15), are simply straight lines with slope λ/σ. The thin grey line at ρ=0 represents the limit cycle, which is kicked, at t= t 0 by P(θ)=sin(θ) with strength ε=1 to the solid curve. After this, the orbits are allowed to evolve under the flow generated by the continuous part of the system. The dashed and dotted curves represent the image of the kicked solid curve under this flow, at times t 1 and t 2 , respectively. The green marker shows how one point, x( t 0 ) evolves under the flow, first to x( t 1 ) and then to x( t 2 ), following the isochron as it relaxes back to the limit cycle. The effect of the shear forces and the subsequent folding, caricatured by the blue arrows can clearly be seen

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