The regularity-chaos-regularity transition in a periodically driven anharmonic oscillator

Bolotin, Yu. L.; Gonchar, V.Yu.; Granovsky, M. Ya.

doi:10.1016/0167-2789(95)00192-7

Cited by 5 publications

(7 citation statements)

References 18 publications

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“…Brandt (1997) proposed from experimental data that ERS system reset could be required in a non linear system (like the cortex) in response to a perturbation such as viewing a flashing light. In systems terms these twin peaks of ERD -ERS do appear conceptually similar to the chaos/regularity transitions which occur when harmonically oscillating linear systems are exposed to non linear amplifications (Bolotin, 1995).…”

Section: When Is the Critical Phase Transition Between Least Action (mentioning

confidence: 79%

Causal Mathematical Logic as a guiding framework for the prediction of “Intelligence Signals” in brain simulations

Lanzalaco

Pissanetzky

2013

Journal of Artificial General Intelligence

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A recent theory of physical information based on the fundamental principles of causality and thermodynamics has proposed that a large number of observable life and intelligence signals can be described in terms of the Causal Mathematical Logic (CML), which is proposed to encode the natural principles of intelligence across any physical domain and substrate. We attempt to expound the current definition of CML, the "Action functional" as a theory in terms of its ability to possess a superior explanatory power for the current neuroscientific data we use to measure the mammalian brains "intelligence" processes at its most general biophysical level. Brain simulation projects define their success partly in terms of the emergence of "non-explicitly programmed" complex biophysical signals such as self-oscillation and spreading cortical waves. Here we propose to extend the causal theory to predict and guide the understanding of these more complex emergent "intelligence Signals". To achieve this we review whether causal logic is consistent with, can explain and predict the function of complete perceptual processes associated with intelligence. Primarily those are defined as the range of Event Related Potentials (ERP) which include their primary subcomponents; Event Related Desynchronization (ERD) and Event Related Synchronization (ERS). This approach is aiming for a universal and predictive logic for neurosimulation and AGi. The result of this investigation has produced a general "Information Engine" model from translation of the ERD and ERS. The CML algorithm run in terms of action cost predicts ERP signal contents and is consistent with the fundamental laws of thermodynamics. A working substrate independent natural information logic would be a major asset. An information theory consistent with fundamental physics can be an AGi. It can also operate within genetic information space and provides a roadmap to understand the live biophysical operation of the phenotype.

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Section: When Is the Critical Phase Transition Between Least Action (mentioning

confidence: 79%

Causal Mathematical Logic as a guiding framework for the prediction of “Intelligence Signals” in brain simulations

Lanzalaco

Pissanetzky

2013

Journal of Artificial General Intelligence

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“…The classical and quantum dynamics of the driven anharmonic oscillator have been investigated extensively [30][31][32]. In the following, we briefly review the classical dynamics of Eq.…”

Section: Modelsmentioning

confidence: 99%

“…In general, for one-body and one-dimensional driven systems with a polynomial potential x 2n , (n > 1), it is known that the energy of the system remains finite even if the dynamics is chaotic [30]. This fact is understood as follows.…”

Section: Modelsmentioning

confidence: 99%

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Divergence of the Floquet-Magnus expansion in a periodically driven one-body system with energy localization

Haga

2019

Phys. Rev. E

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The Floquet-Magnus expansion is a useful tool to calculate an effective Hamiltonian for periodically driven systems. In this study, we investigate the convergence of the expansion for a one-body nonlinear system in a continuous space, a driven anharmonic oscillator. In this model, all eigenstates of the time evolution operator are found to be localized in energy space, and the expectation value of the energy is bounded from above. We first propose a general procedure to estimate the radius of convergence of the Floquet-Magnus expansion for periodically driven systems with an unbounded energy spectrum. By applying it to the driven anharmonic oscillator, we numerically show that the expansion diverges for all driving frequencies even if the anharmonicity is arbitrarily small. This conclusion contradicts the widely accepted belief that the divergence of the Floquet-Magnus expansion is a direct consequence of quantum ergodicity, which implies that each eigenstate of the time evolution operator is a linear combination of all available eigenstates of the unperturbed Hamiltonian and the system heats up to infinite temperature after long intervals.

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“…Resonance overlap criterion allows better understanding of the mechanism of the above mentioned regularity-chaos-regularity transition that exists in any (multi-or single-well) potential with a localized region of instability. Let us use similarity in structure of phase space of the considered two-dimensional autonomous Hamiltonian system with the compact region of negative Gaussian curvature and one-dimensional system with periodic perturbation (3.1) [27].…”

Section: Normal Formsmentioning

confidence: 99%

Regular and Chaotic Classical and Quantum Dynamics in Multi-Well Potentials

Berezovoj,

Bolotin,

Cherkaskiy

et al. 2015

Preprint

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The regularity-chaos-regularity transition in a periodically driven anharmonic oscillator

Cited by 5 publications

References 18 publications

Causal Mathematical Logic as a guiding framework for the prediction of “Intelligence Signals” in brain simulations

Causal Mathematical Logic as a guiding framework for the prediction of “Intelligence Signals” in brain simulations

Divergence of the Floquet-Magnus expansion in a periodically driven one-body system with energy localization

Regular and Chaotic Classical and Quantum Dynamics in Multi-Well Potentials

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