Synchronization
Most of course smallest systems...
Few variables
3 body, Lorenz convection 3 variable
Logistic map one variable.
2 for location 2 for velocity
The surprise was simple system can be very complex.
Large Dynamical Systems -
Complex systems can behave simply in some cases...
Patterns emerge unexpectedly, the system seems to organize itself with no outside intervention.
The individual parts of the system spontaneously cooperate.
Cooperative behavior of huge dynamical systems.
Different parts of a system oscillate in unison.. They synchronize.
We are going to think about the synchronization of periodic things called oscillators,
rather than the synchronization of chaos.
Nature has built many synchronizing systems out of inherently rhythmic devices or rhythmic entities.
Pacemaker cells in heart... 10,000 cells in the sinoatrial node. Each one of them is a competent little oscillator.
It has its own voltage rhythmic.
Must be electrically synchronized to send a coherent signal.
Pacemaker cells not following a leader, they are organizing themselves - self organization - holarchy.
Emerging spontaneously.
Syncronization is a subject?
We can march together, we can sing together, we can dance together
And we can all do it without a leader.
People can clap in sync.
Because we are so good at it, we take it for granted how it actually works.
The phenomenon of spontaneous synchronization is found in circadian rhythms, heart & intestinal muscles, insulin-secreting cells in the pancreas, ambling elephants, drummers drumming, menstrual cycles, and fireflies, among others.
What does it take to get in sync?
-Flocks of birds (proximity)
-Schools of Fish (proximity)
-Fireflies that flash in unison (light)
-Crickets (sound)
-Frogs Ribbit (sound)
- swarming bees
-Pacemaker cells not conscious, but still they can synchonize (currents)
-Circadian Rhythms
-Intestinal muscles
-Insulin secreting cells in pancreas.
-drummers drumming
-Clapping in audience
-Women who are good friends, have their period same time...
Silent chemical communication that (mediate through pheromones)...
Even inanimate can sync
-Electrical circuits (electricity)
-Two grandfather clocks (vibrations)
-Metronomes (vibrations)
-tuning forks
-Laser is coherent … All atoms pulsing in unison all emitting light of one frequency.
It is like nature running the wrong way against entropy...
Huygens - looks at two pendulum clocks - he invented.
Solved the longitude problem at see
Nearly identical... ticking in perfect anitphase.
They are communicating somehow.
They were connected to the same beam...
Metronomes... rolling platform. Like wooden beam in clocks.
As the platform moves it provides a little jiggle that keeps them in sync.
Interaction is mediated by something
Light
Sound
Vibration
Gravity
Electrical force
Pheromones
Proximity
Huge numbers of oscillators.
Nonlinear Dynamics to large populations
Art Winfree same time as Lorenz.
Parallel thing for oscillars.
Needed non-linear oscillators , because biological oscillators always have attractors.
Not just periodic, but they settle into a periodic rhythm with a certain amplitude that is well regulated.
If they are disturbed then it comes back... Whenever you have an attractor, in this case a periodic cycle, you have to have non-linear dynamics (because of the feedback).
Strengthen the attractor by stressing it...
Heart speeds up, body brings it back down...
Linear attractors have boring attractors that are PURE equilibrium.
Waterwheel rocking back and forth.
Nonlinear oscillators... 1000s of interacting non-linear oscillators.
Diverse... Because in fireflies for example, there are genetic differences.
Huge collection of attractor cycle oscillators, diverse in their properties and had a metaphor.
A club of runners... they want to run together.. but some faster than others.
Bell curve of performance...
Narrow the bell curve
Vary diverse ---> Moderately diverse ---> clones
Onset of a sync is a phase transition.
Analog of a phase transition... water is molecules in space. Water freezing is in sync in space
This is a lining up IN TIME
Synchrony breaks out suddenly , NOT gradually.
It is a kind of bifurcation.
Collective behavior of oscillators.
Bifurcation a few years ago on Londons millenium bridge.
Bridge swayed sideways.
Soldiers break step on a bridge.. bridge to resonate.
This is different... Soldiers told to march in step.
People NOT marching in step... no organization initially.
Vertical oscillations with soldiers.
2 cycles per sec is the soldier resonance step... bridge engineers know not to make a bridge.
bridge had a sideways resonance of 1 cycle per sec step... much less force sideways.
Bifurcation like what Winfree found..
150-160 people, bridge suddenly starting oscillating widly
below that crowd desynchronized.
Cooperative behavior of huge dynamical systems.
The support is so light that it can react to the side-to-side motion of the metronomes' arms, thus coupling them weakly. Although seeing the arms swing together is impressive, hearing the "tick-tocks" come into sync is marvelous and adds a lot to the demonstration. From random, to syncopated rhythms, to unison.
As an introduction, it's instructive to demonstrate that the five oscillators (metronomes) are not precisely identical; start them together in synchrony on the FoamCore board just sitting on the lecture bench and watch them soon get out of phase with each other, notwithstanding that they are all set to the same number of bpm. Having shown this, starting them randomly and then observing them phase lock (when supported by the cans) is even more impressive.
Few variables
3 body, Lorenz convection 3 variable
Logistic map one variable.
2 for location 2 for velocity
The surprise was simple system can be very complex.
Large Dynamical Systems -
Complex systems can behave simply in some cases...
Patterns emerge unexpectedly, the system seems to organize itself with no outside intervention.
The individual parts of the system spontaneously cooperate.
Cooperative behavior of huge dynamical systems.
Different parts of a system oscillate in unison.. They synchronize.
We are going to think about the synchronization of periodic things called oscillators,
rather than the synchronization of chaos.
Nature has built many synchronizing systems out of inherently rhythmic devices or rhythmic entities.
Pacemaker cells in heart... 10,000 cells in the sinoatrial node. Each one of them is a competent little oscillator.
It has its own voltage rhythmic.
Must be electrically synchronized to send a coherent signal.
Pacemaker cells not following a leader, they are organizing themselves - self organization - holarchy.
Emerging spontaneously.
Syncronization is a subject?
We can march together, we can sing together, we can dance together
And we can all do it without a leader.
People can clap in sync.
Because we are so good at it, we take it for granted how it actually works.
The phenomenon of spontaneous synchronization is found in circadian rhythms, heart & intestinal muscles, insulin-secreting cells in the pancreas, ambling elephants, drummers drumming, menstrual cycles, and fireflies, among others.
What does it take to get in sync?
-Flocks of birds (proximity)
-Schools of Fish (proximity)
-Fireflies that flash in unison (light)
-Crickets (sound)
-Frogs Ribbit (sound)
- swarming bees
-Pacemaker cells not conscious, but still they can synchonize (currents)
-Circadian Rhythms
-Intestinal muscles
-Insulin secreting cells in pancreas.
-drummers drumming
-Clapping in audience
-Women who are good friends, have their period same time...
Silent chemical communication that (mediate through pheromones)...
Even inanimate can sync
-Electrical circuits (electricity)
-Two grandfather clocks (vibrations)
-Metronomes (vibrations)
-tuning forks
-Laser is coherent … All atoms pulsing in unison all emitting light of one frequency.
It is like nature running the wrong way against entropy...
Huygens - looks at two pendulum clocks - he invented.
Solved the longitude problem at see
Nearly identical... ticking in perfect anitphase.
They are communicating somehow.
They were connected to the same beam...
Metronomes... rolling platform. Like wooden beam in clocks.
As the platform moves it provides a little jiggle that keeps them in sync.
Interaction is mediated by something
Light
Sound
Vibration
Gravity
Electrical force
Pheromones
Proximity
Huge numbers of oscillators.
Nonlinear Dynamics to large populations
Art Winfree same time as Lorenz.
Parallel thing for oscillars.
Needed non-linear oscillators , because biological oscillators always have attractors.
Not just periodic, but they settle into a periodic rhythm with a certain amplitude that is well regulated.
If they are disturbed then it comes back... Whenever you have an attractor, in this case a periodic cycle, you have to have non-linear dynamics (because of the feedback).
Strengthen the attractor by stressing it...
Heart speeds up, body brings it back down...
Linear attractors have boring attractors that are PURE equilibrium.
Waterwheel rocking back and forth.
Nonlinear oscillators... 1000s of interacting non-linear oscillators.
Diverse... Because in fireflies for example, there are genetic differences.
Huge collection of attractor cycle oscillators, diverse in their properties and had a metaphor.
A club of runners... they want to run together.. but some faster than others.
Bell curve of performance...
Narrow the bell curve
Vary diverse ---> Moderately diverse ---> clones
Onset of a sync is a phase transition.
Analog of a phase transition... water is molecules in space. Water freezing is in sync in space
This is a lining up IN TIME
Synchrony breaks out suddenly , NOT gradually.
It is a kind of bifurcation.
Collective behavior of oscillators.
Bifurcation a few years ago on Londons millenium bridge.
Bridge swayed sideways.
Soldiers break step on a bridge.. bridge to resonate.
This is different... Soldiers told to march in step.
People NOT marching in step... no organization initially.
Vertical oscillations with soldiers.
2 cycles per sec is the soldier resonance step... bridge engineers know not to make a bridge.
bridge had a sideways resonance of 1 cycle per sec step... much less force sideways.
Bifurcation like what Winfree found..
150-160 people, bridge suddenly starting oscillating widly
below that crowd desynchronized.
Cooperative behavior of huge dynamical systems.
The support is so light that it can react to the side-to-side motion of the metronomes' arms, thus coupling them weakly. Although seeing the arms swing together is impressive, hearing the "tick-tocks" come into sync is marvelous and adds a lot to the demonstration. From random, to syncopated rhythms, to unison.
As an introduction, it's instructive to demonstrate that the five oscillators (metronomes) are not precisely identical; start them together in synchrony on the FoamCore board just sitting on the lecture bench and watch them soon get out of phase with each other, notwithstanding that they are all set to the same number of bpm. Having shown this, starting them randomly and then observing them phase lock (when supported by the cans) is even more impressive.
Synchronization, Entrainment and Coupling
Synchronization of chaos is a phenomenon that may occur when two, or more, dissipative chaotic systems are coupled.
Synchronization may present a variety of forms depending on the nature of the interacting systems and the type of coupling, and the proximity between the systems.
In general, this reasoning leads to the correct critical coupling value for synchronization.
Entrainment is the process whereby two interacting oscillating systems, which have different periods when they function independently, assume the same period. The two oscillators may fall into synchrony, but other phase relationships are also possible.
The system with the greater frequency slows down, and the other accelerates. Christian Huygens, a notable physicist, coined the term entrainment after he noticed, in 1666, that two pendulum clocks had moved into the same swinging rhythm, and subsequent experiments duplicated this process. Notably, the two pendula stabilized not in synchrony, but in antiphase. They satisfy the definition of entrainment because they have the same period, even though they have opposite phase. The accepted explanation for this is that small amounts of energy are transferred between the two systems when they are out of phase in such a way as to produce negative feedback. As they assume a more stable phase relationship, the amounts of energy gradually reduce to zero. In the realm of physics, entrainment appears to be related to resonance.
In the study of chronobiology, entrainment occurs when rhythmic physiological or behavioral events match their period to an environmental oscillation (termed a zeitgeber, which is German for "timegiver"). The activity/rest (sleep) cycle is only one set of such events that is normally entrained by environmental cues whose period is ultimately determined by the earth's rotation. The term entrainment is justified because the biological rhythms are endogenous: they persist when the organism is isolated from periodic environmental cues. Circadian oscillations occur even in isolated organs, and it is believed that a master pacemaker in the mammalian brain, the SCN (suprachiasmatic nuclei), entrains the periphery. Such hierarchical relationships are not the only ones possible: two or more oscillators may couple in order to assume the same period without either being dominant over the other(s). This situation is analogous to Huygens' pendulum clocks.
Synchronization may present a variety of forms depending on the nature of the interacting systems and the type of coupling, and the proximity between the systems.
In general, this reasoning leads to the correct critical coupling value for synchronization.
Entrainment is the process whereby two interacting oscillating systems, which have different periods when they function independently, assume the same period. The two oscillators may fall into synchrony, but other phase relationships are also possible.
The system with the greater frequency slows down, and the other accelerates. Christian Huygens, a notable physicist, coined the term entrainment after he noticed, in 1666, that two pendulum clocks had moved into the same swinging rhythm, and subsequent experiments duplicated this process. Notably, the two pendula stabilized not in synchrony, but in antiphase. They satisfy the definition of entrainment because they have the same period, even though they have opposite phase. The accepted explanation for this is that small amounts of energy are transferred between the two systems when they are out of phase in such a way as to produce negative feedback. As they assume a more stable phase relationship, the amounts of energy gradually reduce to zero. In the realm of physics, entrainment appears to be related to resonance.
In the study of chronobiology, entrainment occurs when rhythmic physiological or behavioral events match their period to an environmental oscillation (termed a zeitgeber, which is German for "timegiver"). The activity/rest (sleep) cycle is only one set of such events that is normally entrained by environmental cues whose period is ultimately determined by the earth's rotation. The term entrainment is justified because the biological rhythms are endogenous: they persist when the organism is isolated from periodic environmental cues. Circadian oscillations occur even in isolated organs, and it is believed that a master pacemaker in the mammalian brain, the SCN (suprachiasmatic nuclei), entrains the periphery. Such hierarchical relationships are not the only ones possible: two or more oscillators may couple in order to assume the same period without either being dominant over the other(s). This situation is analogous to Huygens' pendulum clocks.