# Nonlinear Systems Posts

## Linear Systems Theory

In this video we will discuss linear systems theory which is based upon the superposition principles of additivity and homogeneity, we will explore both of these principal separately to get a clear...

## Systems Overview

In this module we give an overview to the model of a system that will form the foundations for our discussion on nonlinear systems, we will quickly present the basic concepts from systems theory...

## Nonlinear System

Nonlinear System A nonlinear system is a type of system that defies the superposition principles of homogeneity and additivity. Feedback loops between components within nonlinear systems and over...

## Linear Systems

Linear Systems Linear systems are defined by their adherence to what is called the superposition principles. There are just two superposition principles and they are called homogeneity and...

## Synergies & Interference

Synergies & Interference A synergy is a constructive relation between two or more elements through which value is added by components performing differentiated functions, while also...

## Nonlinear Feedback Loops

Nonlinear Feedback Loops A feedback loop could be defined as a channel or pathway formed by an ‘effect’ returning to its ’cause,’ and generating either more or less of the...

## Bifurcations & Attractors

Bifurcations & Attractors An attractor is a set of states towards which a system will naturally gravitate and remain cycling through unless perturbed. For any given system we can create a...

## Punctuated Equilibrium

Punctuated Equilibrium Punctuated equilibrium is a model first derived from evolutionary biology. This model deals withÂ the dynamicsÂ of a complex system, suggesting that most nonlinear systems...

## Nonlinear Thinking

A line is often defined as the shorts path from one point to another, linear thinking then describes how we interpret events or act in terms of direct cause and effect means. When we use linear...

## Long Tail Distributions

Long Tail Distributions A long tail distribution is one that has very few occurrences of very large events, and very many occurrences of very small events, which gives the graph a “long...

## Exponents & Power Laws

Exponents & Power Laws The term power law describes a functional relationship between two quantities, where one quantity varies as a power – or exponent – of another. Part of the...

## Fractals

Fractals Fractals are both physical phenomenon and mathematical objects, exhibiting a repeating pattern that is displayed at various levels of magnitude, what is called scale invariance, creating...

## Phase Transitions

Phase Transitions Phase transitions and bifurcations are periods of qualitative and often rapid change in the dynamics of a nonlinear systemâ€™s state. They involve positive feedback loops that...

## Butterfly Effect

Butterfly Effect The butterfly effect is a popular term for what is called sensitive dependence on initial conditions in which a small change in some input state to a nonlinear system can result...

## Nonlinear Dynamics & Chaos

Nonlinear Dynamics & Chaos Chaos theory is the study of nonlinear systems dynamics whose development is marked by iteration and feedback loops, making them sensitive to initial conditions...

## Dynamical Systems

Dynamical Systems Within science and mathematics, dynamics is the study of how things change with respect to time. As opposed to describing things simply in terms of their static properties, the...