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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.
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.
The Lotka–Volterra system of equations is an example of a Kolmogorov population model (not to be confused with the better known Kolmogorov equations), [2] [3] [4] which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism.
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.
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 ...
Biological organization spans several scales and are determined based different structures depending on what the system is. [1] Examples of biological systems at the macro scale are populations of organisms. On the organ and tissue scale in mammals and other animals, examples include the circulatory system, the respiratory system, and the ...
Linear chromosomes are also in some ways disadvantageous or problematic, one of the biggest potential issues being the end replication problem. This is a phenomenon which occurs due to the directionality of DNA replication enzymes, resulting in the gradual loss of genetic material at the ends of linear chromosomes after each subsequent cycle of ...
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