Programa de Pós-Graduação em Matemáticahttp://repositorio.ufsm.br/handle/1/23462020-03-28T08:31:00Z2020-03-28T08:31:00ZModelos discretos para agregação populacionalRossato, Marcelo Cargneluttihttp://repositorio.ufsm.br/handle/1/197632020-03-07T06:02:20Z2019-12-12T00:00:00ZModelos discretos para agregação populacional
Rossato, Marcelo Cargnelutti
Rodrigues, Luiz Alberto Díaz
The mechanisms that can lead to the formation of heterogeneous distribution of individuals
of many biological species arouse the interest of researchers from various areas. Many
mathematical models of pattern formation are based on the Turing mechanism and on
aggregation processes in relation to concentration gradients of a chemical substance. Recently,
the Cahn-Hilliard principle of phase separation, which assumes density-dependent
movement, has been used to study self-organized mussel patterns. In this work, we formulate
three discrete models of coupled map networks with density-dependent movement
to describe processes of aggregation and formation of spatial patterns. Some species show
better development at intermediate densities, avoiding problems related to overpopulation
or the difficulty of keeping the species at low population densities. Thus, the first
model considers only the local perception of individuals for movement, while in the other
two it is taken into account that they have a sharper sensory capacity and also analyze
conditions at nearby sites. Several discrete model simulations were performed for several
parameter sets and the continuous formulations corresponding to each one of the models
were obtained. The resulting spatial patterns were classified as homogeneous, stable
heterogeneous, oscillatory heterogeneous or unstable. Thus, we conclude that the three
proposed models can represent aggregation mechanisms and that this process occurred
more effectively considering that individuals can perceive not only the density at their
site, but also at neighboring sites.
Universidade Federal de Santa Maria
Dissertação
2019-12-12T00:00:00ZModelos discretos para dinâmica hospedeiro-parasitoide-predadorSelau, Poliana Kenderli Pacinihttp://repositorio.ufsm.br/handle/1/196672020-02-28T06:02:11Z2019-10-17T00:00:00ZModelos discretos para dinâmica hospedeiro-parasitoide-predador
Selau, Poliana Kenderli Pacini
Mistro, Diomar Cristina
In this work, we formulate discrete models, described by Difference Equations and Coupled
Map Lattices, in order to analize the local and spatio-temporal dynamics of hostparasitoid-
predator dynamics. We firstly consider that the three species reproduce in the
same time scale so that the dynamics is described by three difference equations. In the
second model, we assume that the predator time scale for reproduction is much slower
than the time scale for reproduction of the host and parasitoid species. In this way, the
predator density is constant and the dynamics and be modelled in terms of two difference
equations. We analyze the order of the events of host reproduction, predation, parasitism
and consumers growth for both models. All the proposed models assume the Beverton-
Holt function for host growth and Holling type III functional response for parasitism and
predation; both consumers are considered specialists. By means of numerical simulations,
we found biestability and triestability, besides finding periodic solutions. We finally
introduced the spatial variable and studied the spatio-temporal dynamics. We obtained
homogeneous as well as heterogeneous spatial distribution. The three species local model
forecasts regarding the species persistence are maintained by the corresponding spatial
model. For the model in the wich the predator density is constant, the spatial model
produces heterogeneous distributions generated by three simultaneously stable equilibria.
Keywords: Difference equations, Coupled Map Lattices, Host-parasitoid-predator dynamics,
Biestability
Universidade Federal de Santa Maria
Dissertação
2019-10-17T00:00:00ZExistência, unicidade e estabilidade de solução para um problema termoelástico hiperbólico com domínio não limitado em RPieper, Christian Róger Vilelahttp://repositorio.ufsm.br/handle/1/195902020-02-18T06:01:49Z2019-08-29T00:00:00ZExistência, unicidade e estabilidade de solução para um problema termoelástico hiperbólico com domínio não limitado em R
Pieper, Christian Róger Vilela
Buriol, Celene
Consider the Cauchy Problem which describes the dynamics of linear
rafters vibrations in R subjected to thermal e ects modeled by the Cattaneo
law.
We will focus our attention on obtaining the existence and uniqueness
of the solution and analyzing the asymptotic behavior of such a solution.
In the rst part we will prove the existence and uniqueness of solutions
for the thermoelastic model.
8>
><>>:
utt + uxxxx ����� uxxtt + xx = 0; em R [0;+1)
t + kqx ����� uxxt = 0; em R [0;+1)
qt + q + k x = 0; em R [0;+1)
:
With initial conditions u(x; 0) = u0(x); ut(x; 0) = u1(x); (x; 0) = 0(x);
q(x; 0) = q0(x):
In the second part we nd a decay rate for total energy
E(t) =
1
2 ZR u2
t + u2
tx + u2
xx + 2 + q2 dx
associated with the model described above.
Universidade Federal de Santa Maria
Dissertação
2019-08-29T00:00:00ZO anel de GREEN da álgebra de TAFTPedrotti, Juliana Borgeshttp://repositorio.ufsm.br/handle/1/193512020-01-11T06:01:59Z2019-06-28T00:00:00ZO anel de GREEN da álgebra de TAFT
Pedrotti, Juliana Borges
Flôres, Daiana Aparecida da Silva
The aim of this work is to characterize the Green ring of Taft algebra, denoted by 𝑇�𝑁�(𝑞�),
where 𝑁� is a positive integer greater than 1 and 𝑞� is a primitive root of unity of order
𝑁�. The Green ring, denoted by 𝑟�(𝑇�𝑁�(𝑞�)), is generated by the isomorphism classes [𝑀�]
of finite dimensional 𝑇�𝑁�(𝑞�)-modules with addition given by [𝑀�] + [𝑁�] = [𝑀� ⊕ 𝑁�] and
multiplication given by the tensor product and it has a -basis given by the classes of isomorphisms
of indecomposable finite dimensional 𝑇�𝑁�(𝑞�)-modules. In this work we describe
the indecomposable 𝑇�𝑁�(𝑞�)-modules and the tensorial product between these. From that
we show that 𝑟�(𝑇�𝑁�(𝑞�)) is a commutative ring generated by two elements subject to certain
relations.
Universidade Federal de Santa Maria
Dissertação
2019-06-28T00:00:00Z