Nonlinear Systems Course


This course is designed as an intuitive and non-mathematical introduction to nonlinear systems, it explores a world of both extraordinary chaos where some small event like a butterfly flapping its wings can be amplified into a tornado, but also a world of extraordinary order in the form of fractals, self-similar structures that repeat themselves at various scales, one of nature

Nonlinear Systems Course2019-01-06T14:50:22+00:00

Nonlinear Systems Book


Nonlinear Systems Download Book This book is a voyage into the extraordinary world of nonlinear systems and their dynamics. The primary focus of the book is to provide you with a coherent understanding of the origins and product of nonlinearity and chaos. [...]

Nonlinear Systems Book2019-04-11T14:31:28+00:00

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 time give rise to synergies or interference that make the output to the system less or more than the sum of its parts and thus nonadditive.View Source [...]

Nonlinear System2019-01-11T13:38:16+00:00

Linear Systems


Linear Systems Linear systems are defined by their adherence to what is called the superposition principles.View Source There are just two superposition principles and they are called homogeneity and additivity. Firstly additivity, which states that we can add the effect or output of two systems together and the resulting combined system will be nothing [...]

Linear Systems2019-01-11T13:38:22+00:00

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 coordinating their activities into an integrated system.View Source Due to the value added by the synergistic interaction, the system becomes more than the simple sum of its parts [...]

Synergies & Interference2019-01-11T13:40:33+00:00

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 same effect. An example of this might be a dialogue between two people. What one person says now will affect what the other person will [...]

Nonlinear Feedback Loops2019-01-11T13:40:47+00:00

Bifurcations & Attractors


Bifurcations & Attractors An attractor is a set of states towards which a system will naturally gravitate and remain cycling through unless perturbed.View Source For any given system we can create a state space representing all the possible states that the system might take, the attractor is then a subset of those states that correspond to [...]

Bifurcations & Attractors2019-01-11T13:46:33+00:00

Punctuated Equilibrium


Punctuated Equilibrium Punctuated equilibrium is a model first derived from evolutionary biology.View Source This model deals with the dynamics of a complex system, suggesting that most nonlinear systems exist in an extended period of stasis, which is later punctuated by sudden shifts of radical change. Complex systems are characterized by long periods of stability where negative feedback [...]

Punctuated Equilibrium2019-01-11T13:46:43+00:00

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 tail." This "long tail" is generated by a power law relationship, meaning there is a power relationship between the size of an event [...]

Long Tail Distributions2019-01-11T14:03:59+00:00
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