How can feedback loops lead to emergent behavior in complex systems?

An example is the motion of a school of fish. Each fish can sense the change in water pressure as the fish in front of it alter course. That change in pressure causes them to alter their course which creates a group movement to swarm in one direction or another

Complex systems create a dynamic interplay of forces that can lead to unexpected, novel, and often sophisticated behaviors, demonstrating how complex wholes can be much more than the sum of their parts. Positive or negative feedback, nonlinear actions that produce unexpectedly large effects, pattern formation and even evolutionary change that contributes to the emergence of new species and ecosystems are all possible

In a closed-loop (feedback) control system, the output of the system is monitored by sensors which feed collected data back to the controller which tunes the control in order to maintain preferred output. A continuous feedback loop driving stabilization. IBM’s design of an “Autonomic Manager” is based upon such a feedback loop…but the point is to algorithmically avoid destabilization as perturbation events emerge. Expand that to an IoT - orchestrate 100 billion stabilized devices all capable of handling their own destabilization events. This is where dynamical system theory plays best. Kronecker Dynamical system concepts are ideal to stabilize massive swarms of drones as kronecker matrices utilizing PIF algorithms for stabilization.

Negative feedback loops tend to stabilize the system, countering changes with opposite reactions. When a change occurs in one direction, a negative feedback loop works to decrease the intensity of that change. For example, in climate systems, increased cloud cover due to rising temperatures can reduce solar radiation, thereby cooling the Earth and mitigating the temperature increase.

Complex systems often contain both types of feedback loops, and emergent behavior arises from their interplay. The balance between positive and negative feedback can determine the stability, resilience, and adaptability of the system.

Take a practical example of designing for emergent behavior and consider a practical example in urban planning, specifically in designing a city's transportation network, to illustrate how understanding and manipulating feedback loops can lead to desired emergent behavior in a complex system. By understanding and strategically manipulating the feedback loops in the city's transportation system, urban planners can guide the system towards a state that aligns with the goals of efficiency, sustainability, and user satisfaction. This approach demonstrates the importance of not just designing individual elements of a system, but also considering how they interact and influence each other in a dynamic, complex environment.

I begin by determining what type of dynamical system is in-play because it can translate into a cognitive-AI solution. (Cognitive, Projected or Kronecker dynamical systems). Dynamical system theory is applied in fields of neuroscience and cognitive development (neo-Piagetian theories of cognitive development). *some* researchers believe cognitive development is best represented by physical theories rather than theories based on linguistics and NLP; differential equations being the tool for modeling human behavior. These equations are interpreted to represent an intelligent agent's cognitive trajectory through state space (matrices). State feedback loops are essential to the functioning of such dynamical systems for self-stabilization.

I strongly recommend the work of Shlomi Dolev in the arena of network and graph dynamical system stabilization. The complexity of these systems can be greatly reduced by picking the correct model from the outset - the mathematics of Kronecker Dynamical system matrices is little different from Tensor matrices; meaning it’s a readily accessible topic to anyone steeped in Googles TensorFlow. I can’t say enough about the work of Edsger Dijkstra on the topic of complex system stabilization - it took us 30 years to figure out his “shortest-path algorithm” is a ‘de facto’ self-stabilization algorithm for network packet traffic.