Meditation-Induced Coherence and Crucial Events

Abstract

In this paper we emphasize that 1/f noise has two different origins, one compatible with Laplace determinism and one determined by unpredictable crucial events. The dynamics of heartbeats, manifest as heart rate variability (HRV) time series, are determined by the joint action of these different memory sources with meditation turning the Laplace memory into a strongly coherent process while exerting an action on the crucial events favoring the transition from the condition of ideal 1/f noise to the Gaussian basin of attraction. This theoretical development affords a method of statistical analysis that establishes a quantitative approach to the evaluation of the stress reduction realized by the practice of Chi meditation and Kundalini Yoga.

Keywords: Yoga and Chi meditation; cognition; coherence; criticality; heart rate variability; stress reduction.

Figure 1

Subordinated cosine wave with Ω = 0.8 and μ = 2.8.

Figure 2

Ensemble average of ξ(t), μ = 2.55 (top) and μ = 2.8 (bottom).

Figure 3

Spectra corresponding to μ = 2.55 (top) and μ = 2.8 (bottom).The red lines are the fitting to the numerical results. Top: The red lines at the left of periodicity bumps yield γ = 0.43 to be compared to the theoretical prediction γ = 3 − μ = 0.45. The red lines at the right of the periodicity bump correspond to the prediction γ = 2. Bottom: The red lines at the left of periodicity bumps yield γ = 0.26 to be compared to the theoretical prediction γ = 3 − μ = 0.2. The red lines at the right of the periodicity bump correspond to the prediction γ = 2.

Figure 4

HRV time series of Yoga meditator (Y1), at the top, and the Chi meditator (C2), at the bottom. The vertical red lines denote the time at which the two meditations start.

Figure 5

The power spectra S(ω) of Chi meditators (C1, C2) before, on the right, and during meditation, on the left. In the left panels, the spectra for C1 and C2 meditators consist of significant bumps at ω = 0.34(rad/sec) and ω = 0.38(rad/sec) respectively, each induced by meditation.

Figure 6

The power spectra S(ω) of Kundalini Yoga meditators (Y1, Y2) before, on the right, and during meditation, on the left. Notice the spectra for Y1 and Y2 meditators consist of significant bumps both before and during meditation. The bump shifts for Y1 meditator from ω = 1.89(rad/s) before meditation to ω = 0.4(rad/s) during meditation. Similarly the bump shifts for Y2 meditator from ω = 1.91(rad/s) before meditation to ω = 0.65(rad/s) during meditation.

Figure 7

DEA scaling δ, IPL index μ and ∈² of the HRV time series of eight different participants before and during Chi meditation.

Figure 8

DEA scaling δ, IPL index μ and ∈² of the HRV time series of four different participants before and during Kundalini Yoga meditation.

Figure 9

Correlation rate C(t = |i − j|) of Equation (4) for the subordinated oscillator with Ω = 0.8. From the top, the blue, red and green curves are for μ = 2.8, 2.5 and 2.2 respectively. As μ decreases C(1) decreases as labeled.

Figure 10

Spectra corresponding to cosine with Ω = 0.77 subordinated to an IPL PDF with a changing μ.