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In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
These systems are often very difficult to solve, so modeling of networks as a linear dynamical systems is easier. Linear systems contain no products between xs and are always solvable. They have the following form for all i: = + + + Unfortunately, biological systems are often nonlinear and therefore need nonlinear models.
Linear pathways follow a step-by-step sequence, where each enzymatic reaction results in the transformation of a substrate into an intermediate product. This intermediate is processed by subsequent enzymes until the final product is synthesized. A linear chain of four enzyme-catalyzed steps. A linear pathway can be studied in various ways.
linear pathways only have one enzymatic reaction producing a species and one enzymatic reaction consuming the species. Branched pathways are present in numerous metabolic reactions, including glycolysis, the synthesis of lysine, glutamine, and penicillin, [1] and in the production of the aromatic amino acids. [2] Simple Branch Pathway.
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...
Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations. This list presents nonlinear ordinary differential equations that have been named, sorted by area of interest.
Systems biology can be considered from a number of different aspects. As a field of study, particularly, the study of the interactions between the components of biological systems, and how these interactions give rise to the function and behavior of that system (for example, the enzymes and metabolites in a metabolic pathway or the heart beats).
A system that has the flatness property is called a flat system. Flat systems have a (fictitious) flat output, which can be used to explicitly express all states and inputs in terms of the flat output and a finite number of its derivatives.
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