The biotic pattern of heartbeat intervals

Sabelli, Hector; Messer, J.; Kovacevic, Lazar; Walthall, K.

doi:10.1016/j.ijcard.2009.10.040

Cited by 9 publications

(7 citation statements)

References 10 publications

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“…16, 2 of the bifurcation diagram is shown with respect to changing parameter in the interval ∈ [4. 6,2 ]. As the figure shows, there are at least two windows in the small region.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Investigation of Bifurcations in the Process Equation

Nazarimehr

Jafari

Golpayegani

et al. 2017

Int. J. Bifurcation Chaos

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This paper investigates the different behaviors of the process equation and parameters of their occurrences. The process equation is a multistable one dimensional map with nonlinear feedback and can show various behaviors such as period doubling route to chaos, bios, unstable windows and periodic windows. In this note, we focus on different behaviors of the process equation by a deep look at phase portraits and cobweb plots. Therefore, period doubling route to chaos and unifurcations of the equation are investigated, and also the parameter of its entrance to biotic pattern is discussed. The control parameter for the process equation is g (the coupling constant). In higher , the system shows some unstable and periodic windows among the biotic behaviors. Different patterns of these windows and the reasons of their happenings are investigated mathematically. In addition, some other types of unstable and periodic windows are discussed and Q-curves determine the difference of these windows with the previous ones.

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“…16, 2 of the bifurcation diagram is shown with respect to changing parameter in the interval ∈ [4. 6,2 ]. As the figure shows, there are at least two windows in the small region.…”

Section: Discussionmentioning

confidence: 99%

“…Bios is a rare type of organization containing the ability of creation and physiological regulation [2,27]. It is proposed as a mathematical pattern that is a variation of chaos and identified in heartbeat intervals [1,6,18]. The process equation, which is shown in Eq.…”

Section: Behaviors Of Process Equationmentioning

confidence: 99%

Investigation of Bifurcations in the Process Equation

Nazarimehr

Jafari

Golpayegani

et al. 2017

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

show abstract

“…We first identified Bios as a distinct pattern when studying heartbeat series; this led us to develop analytic methods that demonstrate causality and creativity in empirical processes. Bios is commonly found in natural and human processes: quantum processes [7], the expansion of galaxies and quasars in three surveys [8,9,10] gravitational waves [11], cosmic microwave background radiation [10], DNA [5], physiological processes [5,[12][13][14][15][16][17], animal populations [18] and human populations [5], economic time series [19][20][21] and the prime numbers [22]. Levy et al [23] have already demonstrated Bios in several musical scores; we have expanded this work in this and other publications [24].…”

Section: Introductionmentioning

confidence: 99%

Asymmetry, Symmetry and Beauty

Zeraoulia¹

2011

Models and Applications of Chaos Theory in Modern Sciences

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Asymmetry and symmetry coexist in natural and human processes. The vital role of symmetry in art has been well demonstrated. This article highlights the complementary role of asymmetry. Further we show that the interaction of asymmetric action (recursion) and symmetric opposition (sinusoidal waves) are instrumental in generating creative features (relatively low entropy, temporal complexity, novelty (less recurrence in the data than in randomized copies and complex frequency composition). These features define Bios, a pattern found in musical compositions and in poetry, except for recurrence instead of novelty. Bios is a common pattern in many natural and human processes (quantum processes, the expansion of the universe, gravitational waves, cosmic microwave background radiation, DNA, physiological processes, animal and human populations, and economic time series). The reduction in entropy is significant, as it reveals creativity and contradicts the standard claim of unavoidable decay towards disorder. Artistic creations capture fundamental features of the world.

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“…The empirical studies here reported involve: (1) The demonstration of complex patterns in biological, economic and social processes that display features of creativity (novelty, diversification and temporal complexity) [10][11][12][13] and causality. To reveal creative features in social processes involves (a) the analysis of change and hence of time series; statistical analysis at one period of time that can only reveal static features: (b) their analysis with embedding methods that examine both simple and complex levels of variation; and (c) the comparison of the results obtained with those observed in randomized copies of the data and with causal and stochastic mathematical models.…”

Section: Introductionmentioning

confidence: 99%

Causal Creation in Social Processes: Empirical Analysis and Theoretical Implications

Sabelli¹

2011

TOCSJ

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This article presents empirical evidence for the creativity of social processes, as contrasted to both deterministic and random models of biological and economic phenomena. New methods for the analysis of empirical data indicate that population changes, financial data and other socioeconomic time series display non-periodic, apparently irregular patterns that evolve in time (temporal complexity), increase in diversity (diversification), and repeat less frequently than randomized copies of the data (novelty). Recurrence and autocorrelation measures indicate that these patterns are generated causally, not randomly. These measurements demonstrating causality and creativity in economic, social, and population processes indicate a non-stationary chaotic pattern (Bios) and suggest an alternative to current models that postulate either causal determinism or random change. Causal and creative chaotic patterns (Bios) are also observed in fundamental natural and human processes (quantum processes, cosmological expansion in the distribution of galaxies and quasars, animal populations, and heart and respiratory rates). Mathematical models show that Bios patterns are generated by equations that combine recurring change (recursion), bipolar opposition (e.g. sine functions) and conservation. Consumption and production (demand and supply) are obvious factors accounting for the generation of Bios in economic processes. Generations, sex, nations, races and classes are fundamental oppositions in social processes that may explain the generation of Bios. The extreme sensitivity of Bios to initial conditions' (external inputs) indicates the possibility of modifying the course of social processes, and the need to develop flexible methods rather than planning economic development. To develop such methods, and based on the empirical results here reported, this article articulates a new theory of social organization and change that advances three principles: (1) action (flow of energy in unidirectional time) as the one and only component of both processes and ideas; (2) opposition, both synergic and conflictual, as present in, and organizing, all physical, biological and mental processes; and (3) priority to nature and supremacy to persons as an unavoidable reality and a desirable pattern of action.

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The biotic pattern of heartbeat intervals

Cited by 9 publications

References 10 publications

Investigation of Bifurcations in the Process Equation

Investigation of Bifurcations in the Process Equation

Asymmetry, Symmetry and Beauty

Causal Creation in Social Processes: Empirical Analysis and Theoretical Implications

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