Swarm%20simulation%20using%20anti-Newtonian%20forces

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Swarm simulationusing anti-Newtonian forces

• Vladimir Zhdankin
• Chaos and Complex Systems
• October 6, 2009

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Outline

• Nature
• Overview of observed swarming
• Computer simulation
• Swarming model
• Selected cases
• No predator
• Single predator
• Multiple predators
• Black sheep
• Conclusions

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Swarming in nature

• Birds flocks
• Fish schools
• Insect swarms
• Mammal herds
• Human crowds

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Why swarm?

• Defense from predators
• Confuses predator
• Improves perception
• Lowers predator success rate
• Foraging
• Mating
• Navigation

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Predator options

• Form hunting packs
• Divert a prey away from swarm and catch
• Spread and surround the swarm
• Lead swarm into a trap

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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

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Simulation

• 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

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Anti-Newtonian force

• Term coined by Clint Sprott
• Disobeys Newtons Third Law
• Newtonian forces are equal in magnitude and
  opposite in direction
• Anti-Newtonian forces are equal in magnitude and
  equal in direction

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Circular orbit
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Elliptical orbit
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Precessing orbit
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N-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 obvious
• Attraction to form hunting packs?
• Repulsion to spread and surround rabbits?
• No interaction at all?

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Equations of motion
Can adjust to give predator repulsion instead of
attraction
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Equation parameters

• Agent parameters
• Mass m
• Coefficient of friction b
• Priority p (scales force toward agent)
• Force parameters
• Long-range force power ?
• Short-range repulsion power a
• Usually ? -1 and a -2 works best

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(No Transcript)
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Trivial case (no predator)
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Trivial case (no predator)
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Trivial case equilibria
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Notes on trivial case

• Uninteresting approximation of nature
• For complexity, add other terms
• External potential
• Self-propulsion
• Noise
• Or, introduce a predator

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Single predator
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Single predator - chaotic
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Can the predator win?
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Can the predator win?
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Why not ?0?
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Why not ?0?
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Older equations of motion
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Multiple predators
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Two predators repelling
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Two predators attracting
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Predator packs
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More complicated case
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An unrealistic solution
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A 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?

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Black sheep - greater friction
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Black sheep - higher priority
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Black sheep - increased mass
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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

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Conclusions

• 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 Natures
  complexity

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Acknowledgements

• Clint Sprott

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References

• Images of swarms in nature are from National
  Geographic
• http//photography.nationalgeographic.com/