Anticipating synchrony in dynamical systems using information theory.
Anupam Ghosh1, Samadhan A Pawar1, R I Sujith1
1Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India.
Chaos (Woodbury, N.Y.)
|April 2, 2022
Summary
This study introduces a new information theory measure (R) to predict harmful synchronization in coupled dynamical systems. This early warning system is crucial for applications where synchronization can be detrimental.
Area of Science:
- Nonlinear Dynamics
- Information Theory
- Complex Systems
Background:
- Synchronization is a common phenomenon in coupled dynamical systems.
- While often beneficial, synchronization can be harmful in certain real-world applications.
- Early detection of harmful synchronization is therefore a critical requirement.
Purpose of the Study:
- To propose a reliable measure (R) for the early detection of complete and generalized synchronization.
- To utilize information theory concepts, specifically joint entropy and mutual information, for synchronization detection.
Main Methods:
- Developed a novel measure (R) based on joint entropy and mutual information.
- Validated the measure using numerical simulations of mathematical models.
- Tested the measure with experimental data from turbulent thermoacoustic systems.
Main Results:
- The proposed measure (R) effectively anticipates both complete and generalized synchronizations.
- Demonstrated applicability across various coupled oscillator models, including chaotic systems.
- Confirmed the measure's efficacy with real-world experimental data.
Conclusions:
- The information-theoretic measure (R) provides a reliable method for early warning of harmful synchronization.
- This approach is applicable to diverse coupled dynamical systems, from mathematical models to experimental setups.
- Offers a valuable tool for mitigating risks associated with unwanted synchronization.
More Related Videos
08:42Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
Published on: September 3, 2021
3.2K
05:59Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis
Published on: October 6, 2023
2.8K
Related Concept Videos
01:23Linear time-invariant Systems
499
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
499
01:24BIBO stability of continuous and discrete -time systems
555
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
555
01:21Linear Approximation in Time Domain
133
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
133
01:10Propagation of Uncertainty from Systematic Error
953
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
953
01:26Transmission-Line Differential Equations
443
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
443
01:22Basic Continuous Time Signals
409
Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
409