Chaos theory, catastrophe theory, and complexity are all examples of nonlinear dynamical systems theory or nonlinear science. The central idea is that systems change over time in many possible patterns that we can analyze and evaluate. Events that seem to be random might not be random at all. The specific concepts of nonlinear change, which have mathematical origins, are explained here along with their evolving applications in psychology, biomedical sciences, organizational behavior, and economics.
Basic Dynamics
Attractors are spatial structures where, if an object enters it, it does not leave. Repellors and saddles also fall into this family of dynamics.
Bifurcations are patterns of instability that divide a dynamical field into parts containing different dynamics taking place inside.
Catastrophe Theory
Catastrophes are sudden changes of events. They do not necessarily imply disaster. Theory describes a set of 7 models, although the cusp, one of the simplest is the most commonly used.
Networks represent communication patterns among neurons, people, and larger sociotechnical entities. Many aspects of complex dynamics contribute to their formation and behavior. It's a small world out there!
We have organized them into four broad categories for your convenience. Start anywhere!
SCTPLS sponsors the longest- running annual conference in its topic area. All nonlinear scientists are invited. Explorers meet world-class experts in a convivial supportive environment.
Chaos and Fractals
Many seemingly random events, which are actually chaotic, are predictable with simple equations. They are sensitive to small differences in their initial values, however, producing what is commonly known as the butterfly effect.
Complex Dynamics
Systems in far-from-equilibrium states tend to self-organize: they create their own structures (without anyone's help) to reduce their internal entropy.
Related phenomena include agentbased modeling, emergence, and synchronization.
Research Methods & Recommended Software
We use a variety of time-series analyses for real-time (experimental) data, such as phase-space analysis, recurrance quantification, nonlinear regression, entropy metrics, and symbolic dynamics for pattern detection.
Nonlinear Dynamics, Psychology and Life Sciences the quarterly research journal published by SCTPLS. Refereed, highly rated and widely indexed, NDPLS is an excellent source of current progress and classroom content. Authors are welcome to submit manuscripts on all nonlinear topics involving living systems.
Become a Member
SCTPLS has supported the development of nonlinear science and its applications worldwide through its publications and conferences since 1991. Its members are academics and practitioners who hail from many walks of professional life.

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