Nonlinear Systems Media
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...
Fractals In Pictures
Fractals are a curved or geometric figure, each part of which has similar characteristics as the whole. Fractals are useful in modeling structures, like coastlines or snowflakes, in which similar...
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 with the dynamics of a complex system, suggesting that most nonlinear systems...
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 system’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...