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Swarm simulation using anti-Newtonian forces. Vladimir Zhdankin Chaos and Complex Systems October 6, 2009. Outline. Nature Overview of observed swarming Computer simulation Swarming model Selected cases No predator Single predator Multiple predators Black sheep Conclusions. - PowerPoint PPT Presentation
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Swarm simulationusing anti-Newtonian
forces
Swarm simulationusing anti-Newtonian
forces
Vladimir ZhdankinChaos and Complex Systems
October 6, 2009
Vladimir ZhdankinChaos and Complex Systems
October 6, 2009
OutlineOutline
Nature Overview of observed swarming
Computer simulation Swarming model Selected cases
No predatorSingle predatorMultiple predatorsBlack sheep
Conclusions
Nature Overview of observed swarming
Computer simulation Swarming model Selected cases
No predatorSingle predatorMultiple predatorsBlack sheep
Conclusions
Swarming in natureSwarming in nature Birds flocks Fish schools Insect swarms Mammal herds Human crowds
Birds flocks Fish schools Insect swarms Mammal herds Human crowds
Why swarm?Why swarm? Defense from predators
Confuses predator Improves perception Lowers predator success rate
Foraging Mating Navigation
Defense from predators Confuses predator Improves perception Lowers predator success rate
Foraging Mating Navigation
Predator optionsPredator options Form hunting packs
Divert a prey away from swarm and catch
Spread and surround the swarm Lead swarm into a trap
Form hunting packs Divert a prey away from swarm and catch
Spread and surround the swarm Lead swarm into a trap
How does swarming happen?
How does swarming happen?
Emergence Organization arises from repetition of simple actions
Each individual makes some decisions Chooses optimal distance from neighbors
Aligns with neighbors Reacts to obstacles
Emergence Organization arises from repetition of simple actions
Each individual makes some decisions Chooses optimal distance from neighbors
Aligns with neighbors Reacts to obstacles
SimulationSimulation Model each member as a particle (“agent”)
Model landscape as Cartesian plane Implement force laws
Long range attraction Short range repulsion Friction Anti-Newtonian force between predator and prey
Model each member as a particle (“agent”)
Model landscape as Cartesian plane Implement force laws
Long range attraction Short range repulsion Friction Anti-Newtonian force between predator and prey
Anti-Newtonian forceAnti-Newtonian force
Term coined by Clint Sprott Disobeys Newton’s Third Law
Newtonian forces are equal in magnitude and opposite in
direction Anti-Newtonian forces are equal in magnitude and equal in direction
Term coined by Clint Sprott Disobeys Newton’s Third Law
Newtonian forces are equal in magnitude and opposite in
direction Anti-Newtonian forces are equal in magnitude and equal in direction
Circular orbitCircular orbit
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Elliptical orbitElliptical orbit
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Precessing orbitPrecessing orbit
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n =1,2,3,...N-body anti-Newtonian
problemN-body anti-Newtonian
problem With more bodies, simplest choice is to have no force between similar agents
For swarming, can add Newtonian forces Attractive force between rabbits is natural
Force between foxes is not as obviousAttraction to form hunting packs?Repulsion to spread and surround rabbits?No interaction at all?
With more bodies, simplest choice is to have no force between similar agents
For swarming, can add Newtonian forces Attractive force between rabbits is natural
Force between foxes is not as obviousAttraction to form hunting packs?Repulsion to spread and surround rabbits?No interaction at all?
Equations of motionEquations of motion
Can adjust to give predator repulsion instead of attraction
Equation parametersEquation parameters
Agent parameters: Mass m Coefficient of friction b Priority p (scales force toward agent)
Force parameters: Long-range force power γ Short-range repulsion power α Usually γ = -1 and α = -2 works best
Agent parameters: Mass m Coefficient of friction b Priority p (scales force toward agent)
Force parameters: Long-range force power γ Short-range repulsion power α Usually γ = -1 and α = -2 works best
Trivial case (no predator)
Trivial case (no predator)
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Trivial case (no predator)
Trivial case (no predator)
Trivial case equilibria
Trivial case equilibria
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+aˆ v
Notes on trivial caseNotes on trivial case
Uninteresting approximation of nature
For complexity, add other terms: External potential Self-propulsion Noise
Or, introduce a predator…
Uninteresting approximation of nature
For complexity, add other terms: External potential Self-propulsion Noise
Or, introduce a predator…€
−∇φ
Single predatorSingle predator
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Single predator - chaotic
Single predator - chaotic
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Can the predator win?Can the predator win?
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Can the predator win?Can the predator win?
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Why not γ=0?Why not γ=0?
Why not γ=0?Why not γ=0?
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Older equations of motion
Older equations of motion
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Multiple predatorsMultiple predators
Two predators repelling
Two predators repelling
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Two predators attracting
Two predators attracting
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Predator packsPredator packs
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More complicated caseMore complicated case
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An unrealistic solution
An unrealistic solution
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A black sheepA black sheep
One swarm agent may have handicaps Injured, sick, or weak in nature Higher mass, friction, or priority in simulation
In nature, predators target these prey
Will it happen in simulation?
One swarm agent may have handicaps Injured, sick, or weak in nature Higher mass, friction, or priority in simulation
In nature, predators target these prey
Will it happen in simulation?
Black sheep - greater friction
Black sheep - greater friction
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Black sheep - higher priority
Black sheep - higher priority
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Black sheep - increased massBlack sheep - increased mass
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Emergence in simulation
Emergence in simulation
Swarming maneuvers Unified motion (away from predators) Splitting to confuse predators
Predator actions Diverting one agent away from swarm Capturing the black sheep
All of these come about from using the anti-Newtonian force
Swarming maneuvers Unified motion (away from predators) Splitting to confuse predators
Predator actions Diverting one agent away from swarm Capturing the black sheep
All of these come about from using the anti-Newtonian force
ConclusionsConclusions
Swarming behavior can be approximated by modeling swarm members as particles that obey simple force laws
The anti-Newtonian force plays a critical role in the swarm dynamics
Emergence is responsible for part of Nature’s complexity
Swarming behavior can be approximated by modeling swarm members as particles that obey simple force laws
The anti-Newtonian force plays a critical role in the swarm dynamics
Emergence is responsible for part of Nature’s complexity
AcknowledgementsAcknowledgements
Clint SprottClint Sprott
ReferencesReferences
Images of swarms in nature are from National Geographic: http://photography.nationalgeographic.com/
Images of swarms in nature are from National Geographic: http://photography.nationalgeographic.com/