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Nonlinearity is a peer-reviewed scientific journal published by IOP Publishing and the London Mathematical Society. The journal publishes papers on nonlinear mathematics, mathematical physics , experimental physics , theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance.
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]
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.
Figure 1. Example of a biological network between genes and proteins that controls entry into S phase. However, with knowledge of network interactions and a set of parameters for the proteins and protein interactions (usually obtained through empirical research), it is often possible to construct a model of the network as a dynamical system.
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.
A complex system is a system composed of many components which may interact with each other. [1] Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and, ultimately, for ...
It was established in 2003 as Nonlinearity in Biology, Toxicology and Medicine, obtaining its current name in 2005. It is published by SAGE Publications on behalf of the International Dose-Response Society, of which it is the official journal. [2] Since its founding, the journal's editor-in-chief has been Edward Calabrese (University of ...
Symmetry breaking in pitchfork bifurcation as the parameter ε is varied. ε = 0 is the case of symmetric pitchfork bifurcation.. In a dynamical system such as ¨ + (;) + =, which is structurally stable when , if a bifurcation diagram is plotted, treating as the bifurcation parameter, but for different values of , the case = is the symmetric pitchfork bifurcation.