Related Experiment Video
Updated: Aug 7, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Conserved quantities and adaptation to the edge of chaos
Michael Baym1, Alfred W Hübler
1Santa Fe Institute, New Mexico 87501, USA.
Abstract:
Certain dynamical systems, such as the shift map and the logistic map, have an edge of chaos in their parameter spaces. On one side of this edge, the dynamics are chaotic for many parameter values, on the other side of the edge they are periodic. We find that discrete-time dynamical systems with wavelet filtered feedback from the dynamical variable to the parameters are attracted to a narrow parameter range near the edge of chaos, the periodic boundary regime. We show that the migration from the chaotic regime to the periodic boundary regime can be attributed to a conserved quantity, and find that such adaptation to the edge of chaos is accompanied by a depopulation of the chaotic regime. We use this conserved quantity to determine the location of the periodic boundary regime and show that its size is proportional to the size of the feedback. Further, we compute the dynamics of the probability density for the parameter for a specific example.
Related Concept Videos
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Conservation of Mass in Finite Cotrol Volume
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
Conservation of Energy in Control Volume
For steady flow systems, the time derivative of the stored energy becomes zero since there is no energy accumulation within the control volume. This simplifies the energy equation to:
Conservation of Mass in Fixed, Nondeforming Control Volume
In the case of a sewer pipe, which can be modeled...
Conservation of Energy
Stability of Equilibrium Configuration
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
