Chaotic Dynamics and Synchronization of von Bertalanffy’s Growth Models

Rocha, J. Leonel; Aleixo, Sandra M.; Caneco, Acilina

doi:10.1007/978-3-319-16118-1_30

Cited by 4 publications

(3 citation statements)

References 21 publications

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“…Successful interregional communication depends on the transient synchronization between harmonization of multiple oscillatory components into an integrated signal through phase-coordinated local neuronal spiking 9 , where the phase of one oscillation modulates in harmony with amplitude fluctuations in another oscillation. Widespread slow of coupled chaotic oscillations modulate faster oscillations of local events 10 , 11 . This is a chaotic system that synchronizes suddenly and completely from one global activity pattern state to another with a minimum duration of transient "phase transition fluctuations".…”

Section: Discussionmentioning

confidence: 99%

The entropy of chaotic transitions of EEG phase growth in bipolar disorder with lithium carbonate

Demirer

Kesebir

2021

Sci Rep

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The application of chaos measures the association of EEG signals which allows for differentiating pre and post-medicated epochs for bipolar patients. We propose a new approach on chaos necessary for proof of EEG metastability. Shannon entropies of concealed patterns of Schwarzian derivatives from absolute instantaneous frequency transformations of EEG signals after Hilbert transform are compared and found significantly statistically different between pre and post-medication periods when fitted to von Bertalanffy’s functions. Schwarzian dynamics measures was compared at first baseline and then at the end of the first hour of one dose 300 mg lithium carbonate intake for the same subject in depressive patients. With an application of Schwarzian derivative on the prediction of von Bertalanffy’s models, integration and segregation of phase growth orbits of neural oscillations can be understood as an influence of chaos on the mixing of frequencies. A phase growth constant parameter was performed to determine the bifurcation parameter of von Bertalanffy’s model at each given non-overlapped EEG segment. Schwarzian derivative was sometimes very close positive near the origin but stayed negative for most of the number of segments. Lithium carbonate changed the chaotic invariants of the EEG Schwarzian dynamics and removed sharp boundaries in the bipolar spectrum.

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Section: Discussionmentioning

confidence: 99%

The entropy of chaotic transitions of EEG phase growth in bipolar disorder with lithium carbonate

Demirer

Kesebir

2021

Sci Rep

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“…Successful Neither can escape the other, so that stable aperiodic oscillation persists. If the three parts are disconnected, the chaos in the model disappears 11 .…”

Section: Discussionmentioning

confidence: 99%

Entropy of Chaotic Transitions of EEG Phase Growth in Bipolar Disorder With Lithium Carbonate

Demirer

Kesebir

2021

Preprint

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The application of chaos theory measures in the association of EEG signals which allows for differentiating pre and postmedicated epochs for bipolar patients. We propose a new approach on positive Schwarzian chaos necessary for a proof of EEG power spectrum of metastability. Shannon entropies of those concealed patterns of positive Schwarzian derivatives from canonical angle transformations of EEG phases from Hilbert transform are compared and found significantly statistical different between pre and post medication periods. Entropy change of chaotic transition measures were compared at first baseline and then at the end of first hour of 300 mg lithium carbonate intake for the same subject in depressive patients. With an application of Schwarzian derivative on the prediction of the von Bertalanffy’s models, integration and segregation of phase growth orbits of neural oscillations can be understood as an influence of chaos on mixing of frequencies. A first order curve-fitting function was performed to determine bifurcation parameter of von Bertalanffy’s model at each given overlapped EEG segment. Schwarzian derivative was positive near the origin which revealed robust chaos. We founded that treatment with Lithium carbonate significantly altered Schwarzian spectrum of chaotic structure and entropy change in Schwarzian amplitudes even though it was not observed in classical EEG power spectrum. Lithium carbonate reduced the strong chaos spectrum of EEG Schwarzian dynamics and removed sharp boundaries in bipolar spectrum.

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“…Our goal is to classify those manifolds based on a different kind of entropy measure, on each unimodal map, . In a transitive Anosov diffeomorphism i.e higher order instantaneous frequencies there exists a unique SRB (Sınai, Ruelle and Bowen) measure supported on a phase gradient cone manifold, is of full volume in a basin which supports all beta-gamma frequencies transitions i.e phase gradients and higher order phase gradients in a cone basin 22,23 .…”

Section: Electroencephalography and Mathematical Approachmentioning

confidence: 99%

Reclassification of Mood Disorders with Comorbid Medical Diseases based on Sinai-Ruelle-Bowen/ SRB Entropy Measures

Kesebir,

Demirer

2023

MRAJ

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Background: Current classification systems ignore the family histories of patients and psychiatric and medical comorbidity. Methods: We study a new approach of applying spectral clustering to determine distinct bipolar disorder subtypes, which is data whose clusters are of various sizes and densities. We discovered clusters by processing a SRB (Sinai-Ruelle-Bowen) similarity matrix that reflects the proximity of Von Bertalanffy’s functions fitted to phase growth dynamics of EEG (electroencephalography) within a new pipeline architecture. For this purpose, 109 patients diagnosed with bipolar disorder according to DSM-V (Diagnostic and Statistical Manual of Mental Disorders, fifth edition) were evaluated in remission period cross-sectionally. Results: We found three distinct bipolar disorder subtypes with the p-values < 0.001. We exhibit mixing sub-shifts of EEG phase gradients such that there are chaotic phase transitions but higher order phase gradients in a cone basin is always strictly convex. More surprisingly, we show that the SRB entropy measures on some time interval although there exist several equilibrium states each corresponds to equilibrium state. Conclusion: It seems subtypes of the bipolar spectrum were shaped according to seasonality, comorbidity for anxiety disorder and presence of psychotic symptom.

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Chaotic Dynamics and Synchronization of von Bertalanffy’s Growth Models

Cited by 4 publications

References 21 publications

The entropy of chaotic transitions of EEG phase growth in bipolar disorder with lithium carbonate

The entropy of chaotic transitions of EEG phase growth in bipolar disorder with lithium carbonate

Entropy of Chaotic Transitions of EEG Phase Growth in Bipolar Disorder With Lithium Carbonate

Reclassification of Mood Disorders with Comorbid Medical Diseases based on Sinai-Ruelle-Bowen/ SRB Entropy Measures

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