When Small Changes Have a Global Impact Joseph Tranquillo Biomedical Engineering Department Bucknell University

How can simple rules lead to complex systems? How can small changes make a big difference in the behavior of a complex system? Questions

Simple rules lead to … 1)Gravity will try to pull a block to the floor 2)No block can occupy the same space as another block 1)Any active cell with 2 or 3 active neighbors will be active next time 2)Any inactive cell with 3 active neighbors will be active next time Falling Blocks The Game of Life

… complex systems Complexity arises because: 1) Many players are following simple rules 2) Conflicting rules create competing demands 1)Many possible ways to balance the competing demands 2)Not clear which balance will result Results:

Small changes can make a big difference A imbalance can be made by: 1)Small disturbances that add up 2) Subtle changes to the competing demands - Rules or numbers of players If put out of balance, a system will find a new balance

What does this mean for a complex system? A complex system may have many balance points A small change can cause the system to become unbalanced An unbalanced system will try to become balanced again It is not always easy to predict what the new balance will be Applications to many systems: Environmental, Biological, Economic, Political, Legal Cultural, Ecological, Astronomical, Ethical, Internet, …

What does this mean to me? It is hard to predict the importance of a single action