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In control theory, a continuous linear time-invariant system (LTI) is exponentially stable if and only if the system has eigenvalues (i.e., the poles of input-to-output systems) with strictly negative real parts (i.e., in the left half of the complex plane). [1]
This entry will describe the popular concepts as well as development of the plateau principle as a scientific, mathematical model. In the sciences, the broadest application of the plateau principle is creating realistic time signatures for change in kinetic models (see Mathematical model). One example of this principle is the long time required ...
The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge. The idea of Lyapunov stability can be extended to infinite-dimensional manifolds, where it is known as structural stability, which concerns the behavior of different but "nearby" solutions to differential equations.
Biological exponential growth is the unrestricted growth of a population of organisms, occurring when resources in its habitat are unlimited. [1] Most commonly apparent in species that reproduce quickly and asexually , like bacteria , exponential growth is intuitive from the fact that each organism can divide and produce two copies of itself.
Biological thermodynamics (Thermodynamics of biological systems) is a science that explains the nature and general laws of thermodynamic processes occurring in living organisms as nonequilibrium thermodynamic systems that convert the energy of the Sun and food into other types of energy.
Modelling biological systems is a significant task of systems biology and mathematical biology. [a] Computational systems biology [b] [1] aims to develop and use efficient algorithms, data structures, visualization and communication tools with the goal of computer modelling of biological systems.
In chemistry, transition state theory (TST) explains the reaction rates of elementary chemical reactions. The theory assumes a special type of chemical equilibrium (quasi-equilibrium) between reactants and activated transition state complexes. [1] TST is used primarily to understand qualitatively how chemical reactions take place.
This open system allows researchers to maintain the exponential growth phase of cells for use in physiological experiments. [ 1 ] A chemostat (from chem ical environment is stat ic) is a bioreactor to which fresh medium is continuously added, while culture liquid containing left over nutrients, metabolic end products and microorganisms is ...