nonlinear systems theory

Nonlinear systems theory studies systems where outputs are not directly proportional to inputs, meaning small changes can lead to unpredictable or complex behaviors. Unlike linear systems, which follow straightforward rules, nonlinear systems can exhibit phenomena like chaos, multiple stable states, and intricate patterns. This theory helps us understand diverse real-world processes—like weather, ecosystems, or the human brain—where relationships are interconnected and dynamic. It provides tools to analyze, predict, and sometimes control behaviors that aren’t simple or predictable, revealing the complex nature of many natural and engineered systems.