Non-Linearity

In a complex system, the behavior of the system as a whole is not simply a linear sum of the behaviors of its individual elements. Instead, the interactions between the elements can lead to emergent properties and behaviors that are nonlinear and often exhibit non-proportional relationships.

These Non-Linearity can be characterized by several factors:

• State transitions : Irreversible. An example of state transitions can be found in a chemical reaction. Consider a system where a reactant slowly combines with another reactant to form a product., landslide
• Small changes can have large impacts :  The butterfly effect is a concept that states that "small causes can havemlarger effects". (introduced by Edward Lorentz). , stone can change river flow
  The sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. 
• Scaleless behavior (fractals) : Exhibit similar patterns regardless of the scale of observation. For example- COVID-19
• Tipping points : A critical threshold or boundary within a complex system where a small change or perturbation can lead to significant and sometimes irreversible shifts in the system's behavior or state. The moment of transition from a stable population to an unstable population is the tipping point.

Non-linearity due to interdependency of element, system, can show different level of non-liniear behaviour

Financial Markets: Small changes in investor sentiment can trigger large swings in stock prices due to non-linear interactions and herd behavior.

Climate Change: The Earth's climate system exhibits non-linear behavior. Small changes in greenhouse gas concentrations can lead to significant and potentially irreversible changes in global temperature patterns.

Ecosystem Collapse: Overfishing or deforestation can push an ecosystem past a tipping point, leading to a rapid decline in biodiversity.