Digital Evolution for Ecology Research: A Review

In digital evolution, populations of computational organisms evolve via the same principles that govern natural selection in nature. These platforms have been used to great effect as a controlled system in which to conduct evolutionary experiments and develop novel evolutionary theory. In addition to their complex evolutionary dynamics, many digital evolution systems also produce rich ecological communities. As a result, digital evolution is also a powerful tool for research on eco-evolutionary dynamics. Here, we review the research to date in which digital evolution platforms have been used to address eco-evolutionary (and in some cases purely ecological) questions. This work has spanned a wide range of topics, including competition, facilitation, parasitism, predation, and macroecological scaling laws. We argue for the value of further ecological research in digital evolution systems and present some particularly promising directions for further research.

Optimal control of nonlocal fractional evolution equations in the α-norm of order $(1,2)$

This paper investigates the optimal control for a class of nonlocal fractional evolution equations of order $\gamma \in (1,2)$ γ ∈ ( 1 , 2 ) in Banach spaces. An adequate definition of α-mild solutions is obtained and the existence, uniqueness and continuous dependence of α-mild solutions for the presented control system are also established. The existence of optimal pairs of nonlocal fractional evolution systems is also demonstrated with a view on the construction of the Lagrange problem. Finally, an example is propounded for the presentation of optimal control.

Controllability of nonlinear fractional evolution systems in Banach spaces: A survey

<p style='text-indent:20px;'>This paper presents a survey for some recent research on the controllability of nonlinear fractional evolution systems (FESs) in Banach spaces. The prime focus is exact controllability and approximate controllability of several types of FESs, which include the basic systems with classical initial and nonlocal conditions, FESs with time delay or impulsive effect. In addition, controllability results via resolvent operator are reviewed in detail. At last, the conclusions of this work and the research prospect are presented, which provides a reference for further study.</p>

Association and other forms of positive dependence for Feller evolution systems

Приведены условия, обеспечивающие положительную ассоциированность для широкого класса неоднородных марковских процессов, называемых феллеровскими процессами эволюции (ФПЭ) и скачкообразными феллеровскими процессами эволюции (СФПЭ). Общие ФПЭ можно исследовать при помощи их (обобщенных) генераторов, зависящих от времени и пространства состояний. Мы будем использовать (обобщенные) генераторы, зависящие от времени и пространства состояний, и меры Леви, зависящие от времени и пространства состояний, для описания положительной ассоциированности общих ФПЭ и СФПЭ соответственно. В завершение, мы покажем применения этих результатов к аддитивным процессам, которые являются неоднородными по времени процессами Леви и часто появляются в качестве полезных примеров в финансовых моделях.