The uniqueness and stability of travelling fronts of competitive systems with different diffusive coefficients

2018 ◽  
Vol 84 (1) ◽  
pp. 171-196
Author(s):  
Yang Wang ◽  
Lingling Shi ◽  
Guirong Liu ◽  
Zhaohai Ma
Resources ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 65 ◽  
Author(s):  
Nicoletta Patrizi ◽  
Valentina Niccolucci ◽  
Riccardo Pulselli ◽  
Elena Neri ◽  
Simone Bastianoni

One of the main goals of any (sustainability) indicator should be the communication of a clear, unambiguous, and simplified message about the status of the analyzed system. The selected indicator is expected to declare explicitly how its numerical value depicts a situation, for example, positive or negative, sustainable or unsustainable, especially when a comparison among similar or competitive systems is performed. This aspect should be a primary and discriminating issue when the selection of a set of opportune indicators is operated. The Ecological Footprint (EF) has become one of the most popular and widely used sustainability indicators. It is a resource accounting method with an area based metric in which the units of measure are global hectares or hectares with world average bio-productivity. Its main goal is to underline the link between the (un)sustainability level of a product, a system, an activity or a population life style, with the land demand for providing goods, energy, and ecological services needed to sustain that product, system, activity, or population. Therefore, the traditional rationale behind the message of EF is: the larger EF value, the larger environmental impact in terms of resources use, the lower position in the sustainability rank. The aim of this paper was to investigate if this rationale is everywhere opportune and unambiguous, or if sometimes its use requires paying a special attention. Then, a three-dimensional modification of the classical EF framework for the sustainability evaluation of a product has been proposed following a previous work by Niccolucci and co-authors (2009). Finally, the potentialities of the model have been tested by using a case study from the agricultural context.


Author(s):  
S. A. Gourley ◽  
M. A. J. Chaplain

In this paper we study travelling front solutions of a certain food-limited population model incorporating time-delays and diffusion. Special attention is paid to the modelling of the time delays to incorporate associated non-local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times. For a particular class of delay kernels, existence of travelling front solutions connecting the two spatially uniform steady states is established for sufficiently small delays. The approach is to reformulate the problem as an existence question for a heteroclinic connection in R4. The problem is then tackled using dynamical systems techniques, in particular, Fenichel's invariant manifold theory. For larger delays, numerical simulations reveal changes in the front's profile which develops a prominent hump.


Entropy ◽  
2013 ◽  
Vol 16 (1) ◽  
pp. 1-22 ◽  
Author(s):  
A. Klimenko
Keyword(s):  

2020 ◽  
Vol 40 (3) ◽  
pp. 1621-1663 ◽  
Author(s):  
Mats Gyllenberg ◽  
◽  
Jifa Jiang ◽  
Lei Niu ◽  
Ping Yan ◽  
...  

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