Complex system

A complex system is a system made up of many parts that interact with each other. Examples of complex systems include Earth's global climate, living organisms, the human brain, and large infrastructure projects like power grids. These systems can also include things like transportation networks, cities, ecosystems, and even the entire universe.

Because these systems have many interacting parts, their behavior is often hard to predict. They can show surprising patterns, adapt to changes, and create order without being told what to do. Scientists study complex systems to understand how the many small parts work together to create the whole system.

The study of complex systems brings together ideas from many different areas of science and math. It includes learning about how things organize themselves, how small changes can lead to big effects, and how systems can adapt and survive. This helps us understand everything from weather patterns to how societies grow and change.

Types of systems

Complex systems can be different kinds, such as complex adaptive systems, which can change and learn over time. Others are polycentric systems, where many parts work together but also make their own decisions.

There are also disorganised systems, where many small interactions happen without forming a clear pattern, and hierarchical systems, which are made of smaller parts that fit together like Russian nesting dolls. Finally, there are cybernetic systems, which use information and feedback to control and adjust themselves.

Key concepts

Complex adaptive systems are special types of complex systems that can change and learn from experience. Examples include international trade markets, social insect and ant colonies, the biosphere and the ecosystem, the brain and the immune system, the cell and the developing embryo, cities, manufacturing businesses, and human social groups like political parties or communities.

A system is decomposable if its parts work independently from each other, like in the model of a perfect gas. In a nearly decomposable system, the parts are mostly independent but still affect each other in small ways, which is common in social systems.

Features

Graphical representation of alternative stable states and the direction of critical slowing down prior to a critical transition (taken from Lever et al. 2020). Top panels (a) indicate stability landscapes at different conditions. Middle panels (b) indicate the rates of change akin to the slope of the stability landscapes, and bottom panels (c) indicate a recovery from a perturbation towards the system's future state (c.I) and in another direction (c.II).

Complex systems are usually open systems, meaning they exist in a thermodynamic gradient and dissipate energy. They are often far from energetic equilibrium, yet they can maintain stable patterns through their interactions.

These systems can experience sudden changes called critical transitions. These shifts happen when conditions pass a certain point, leading to abrupt changes in the system's state. Complex systems can also be nested, where smaller systems make up larger ones, like how an economy is made of organisations, which are made of people, and so on. They often form dynamic networks with many local connections and a few longer-range links. One key feature is that they can produce emergent behaviors—properties that arise from the interactions of many smaller parts and can only be understood by looking at the system as a whole. For instance, the way termites build mounds is an emergent property of their collective behavior. Additionally, complex systems often have non-linear relationships, where small changes can lead to large, unexpected effects, and they include feedback loops that can either dampen or amplify changes within the system.

History

In 1948, Dr. Warren Weaver wrote about how science deals with simple and complex problems. He explained that some problems have many connected parts working together.

The study of complex systems became more popular in the 1970s. In 1984, the Santa Fe Institute was created to study these systems. Many famous scientists have worked there. In 2021, the Nobel Prize in Physics was given to three scientists for their work on understanding complex systems, which helped improve climate models.

Applications

The traditional way to handle complicated systems is to break them into smaller, separate parts. For example, companies split their work into different departments, and engineers design systems using separate modules. However, when problems occur between these parts, the whole system can fail.

Cities are complex systems where many factors interact. When cities are simplified too much, they often stop working well. In healthcare, complexity helps us understand how different groups like doctors, patients, and policymakers work together. In biology, studying complexity helps us understand how living things, like our bodies, function. Complex systems are also linked to chaos theory, which looks at systems that behave unpredictably. The study of complexity shows how many detailed interactions can create simple patterns, and these systems often change over time in important ways.

Complex systems can often be shown as networks. For example, the Internet is a network of computers connected by links. Other examples include social networks, financial systems, airline routes, and biological systems.

Notable scholars

Many smart people have studied complex systems. These are just a few of them: