Related papers: Evolutionary Equations
These are the notes from my courses on the arithmetic of quadratic forms.
This, fourth paper of the series (see previous papers in Refs.[1-3]) derives approximate equations for future numerical studies of initial evolution of hurricanes, develops new analytical models of hurricane genesis and maturing, and…
We present the explicit formulae, describing the structure of symmetries and formal symmetries of any scalar (1+1)-dimensional evolution equation. Using these results, the formulae for the leading terms of commutators of two symmetries and…
In the spirit of the many recent simple models of evolution inspired by statistical physics, we put forward a simple model of the evolution of such models. Like its objects of study, it is (one supposes) in principle testable and capable of…
Comment on ``The 2005 Neyman Lecture: Dynamic Indeterminism in Science'' [arXiv:0808.0620]
Comment on ``The 2005 Neyman Lecture: Dynamic Indeterminism in Science'' [arXiv:0808.0620]
This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985-2009. Rather than modeling the network cumulatively, this…
We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the…
This paper attempts to connects the evolution of computer languages with the evolution of life, where the later has been dictated by \emph{theory of evolution of species}, and tries to give supportive evidence that the new languages are…
Explicit coupling property and gradient estimates are investigated for the linear evolution equations on Hilbert spaces driven by an additive cylindrical L\'evy process. The results are efficiently applied to establish the exponential…
A short review of the recent results and models of complex networks.
Evolutionary computation (EC), as a powerful optimization algorithm, has been applied across various domains. However, as the complexity of problems increases, the limitations of EC have become more apparent. The advent of large language…
This version has been withdrawn. The new and final version is on ArXiv 1103.4878
We study a model of a multi-species ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law…
The purpose of this paper is to present a method of solving the Shr\"odinger Equation (SE) by Genetic Algorithms and Grammatical Evolution. The method forms generations of trial solutions expressed in an analytical form. We illustrate the…
A list of forty third-order exactly integrable two-field evolutionary systems is presented. Differential substitutions connecting various systems from the list are found. It is proved that all the systems can be obtained from only two of…
In this revised version, we add some expository material and references and make some minor corrections.
In this paper, we consider energy decay estimates for the following nonlinear evolution problem $$\begin{split} [P(u_t(t))]_t + A u(t) + B(t , x , u_t(t)) =0,\quad t\in J=(0,\infty), \end{split}$$ under suitable assumptions on the…
These lecture notes provide an elementary introduction, within the framework of finite quantum systems, to recent developments in the theory of entropic fluctuations.
We consider stochastic equations for the class of formal mappings. Existence and uniqueness of solution, as well as evolution property are proved.