Bifurcation theoryBifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior.
Business analysisBusiness analysis is a professional discipline focused on identifying business needs and determining solutions to business problems. Solutions may include a software-systems development component, process improvements, or organizational changes, and may involve extensive analysis, strategic planning and policy development. A person dedicated to carrying out these tasks within an organization is called a business analyst or BA. Business analysts are not found solely within projects for developing software systems.
Dissipative systemA dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter. A tornado may be thought of as a dissipative system. Dissipative systems stand in contrast to conservative systems. A dissipative structure is a dissipative system that has a dynamical regime that is in some sense in a reproducible steady state. This reproducible steady state may be reached by natural evolution of the system, by artifice, or by a combination of these two.
Functional requirementIn software engineering and systems engineering, a functional requirement defines a function of a system or its component, where a function is described as a summary (or specification or statement) of behavior between inputs and outputs. Functional requirements may involve calculations, technical details, data manipulation and processing, and other specific functionality that define what a system is supposed to accomplish. Behavioral requirements describe all the cases where the system uses the functional requirements, these are captured in use cases.
Minimum viable productA minimum viable product (MVP) is a version of a product with just enough features to be usable by early customers who can then provide feedback for future product development. A focus on releasing an MVP means that developers potentially avoid lengthy and (possibly) unnecessary work. Instead, they iterate on working versions and respond to feedback, challenging and validating assumptions about a product's requirements. The term was coined and defined in 2001 by Frank Robinson and then popularized by Steve Blank and Eric Ries.
Poincaré recurrence theoremIn mathematics and physics, the Poincaré recurrence theorem states that certain dynamical systems will, after a sufficiently long but finite time, return to a state arbitrarily close to (for continuous state systems), or exactly the same as (for discrete state systems), their initial state. The Poincaré recurrence time is the length of time elapsed until the recurrence. This time may vary greatly depending on the exact initial state and required degree of closeness. The result applies to isolated mechanical systems subject to some constraints, e.
PredictabilityPredictability is the degree to which a correct prediction or forecast of a system's state can be made, either qualitatively or quantitatively. Causal determinism has a strong relationship with predictability. Perfect predictability implies strict determinism, but lack of predictability does not necessarily imply lack of determinism. Limitations on predictability could be caused by factors such as a lack of information or excessive complexity. In experimental physics, there are always observational errors determining variables such as positions and velocities.
Gaia hypothesisThe Gaia hypothesis (ˈɡaɪ.ə), also known as the Gaia theory, Gaia paradigm, or the Gaia principle, proposes that living organisms interact with their inorganic surroundings on Earth to form a synergistic and self-regulating, complex system that helps to maintain and perpetuate the conditions for life on the planet. The Gaia hypothesis was formulated by the chemist James Lovelock and co-developed by the microbiologist Lynn Margulis in the 1970s.
Structural stabilityIn mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by small perturbations (to be exact C1-small perturbations). Examples of such qualitative properties are numbers of fixed points and periodic orbits (but not their periods). Unlike Lyapunov stability, which considers perturbations of initial conditions for a fixed system, structural stability deals with perturbations of the system itself.
Orbit (dynamics)In mathematics, specifically in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system. It can be understood as the subset of phase space covered by the trajectory of the dynamical system under a particular set of initial conditions, as the system evolves. As a phase space trajectory is uniquely determined for any given set of phase space coordinates, it is not possible for different orbits to intersect in phase space, therefore the set of all orbits of a dynamical system is a partition of the phase space.
