A multifunctional central pattern generator (CPG) can produce bursting polyrhythms that determine locomotive activity in an animal: for example, swimming and crawling in a leech. Each rhythm corresponds to a specific attractor of the CPG. We employ a Hodgkin-Huxley type model of a bursting leech heart interneuron, and connect three such neurons by fast inhibitory synapses to form a ring. This network motif exhibits multistable co-existing bursting rhythms. The problem of determining rhythmic outcomes is reduced to an analysis of fixed points of Poincare mappings and their attractor basins, in a phase plane defined by the interneurons' phase differences along bursting orbits. Using computer assisted analysis, we examine stability, bifurcations of attractors, and transformations of their basins in the phase plane. These structures determine the global bursting rhythms emitted by the CPG. By varying the coupling synaptic strength, we examine the dynamics and patterns produced by inhibitory networks.

What changes in our brain when we learn? This is perhaps the most intriguing question of science in this century. In an attempt to learn more about the inner workings of neural circuitry, I studied cultured 2-dimensional networks of neurons on multi-electrode arrays (MEAs). MEAs are ideal tools for studying long-term neural ensemble activity because many individual cells can be studied continuously for months, through electrical stimulation and recording. One of the most prominent patterns of activity observed in these cultures is network-wide spontaneous bursting, during which most of the active electrodes in the culture show elevated firing rates. We view the persistence of spontaneous bursting in vitro as a sign of arrested development due to deafferentation. Substituting distributed electrical stimulation for afferent input transformed the activity in dissociated cultures from bursting to more dispersed spiking, reminiscent of activity in the adult brain. Burst suppression reduced the variability in neural responses making it easier to induce and detect functional plasticity caused by tetanic stimulation. This suggests that spontaneous bursts interfere with the effects of external stimulation and that a burst-free environment leads to more stable connections and predictable effects of tetanization. Moreover, our culture models continuously receive input stimulation in the form of background electrical stimulation, and so better resemble the intact brain than isolated (non-continuously stimulated) cultures. The proportion of GABAergic neurons in the cultures was significantly increased (p<1e-2, paired t-test) after burst-quieting for 2 days, suggesting that burst suppression operated through the homeostatic control of inhibitory neurotransmitter levels. We also studied the role of spontaneous bursts as potential carriers of information in the network by clustering these spatiotemporally diverse bursts. Spontaneous burst clusters were stable over hours and tetanic stimulation significantly reorganized the distribution of the clusters. In summary, this body of work explores the rules of network-level functional plasticity and provides the input (electrical stimulation) output (spatiotemporal patterns) mappings for behavioral studies in embodied hybrid systems. The results of this study may also have clinical implications in the development of sensory prostheses and treatment of diseases of aberrant network activity such as epilepsy.

Thesis (Ph. D.)--University of Notre Dame, 2006. / Thesis directed by Steven M. Boker for the Department of Psychology. "December 2006." Includes bibliographical references (leaves 99-102).

Thesis (Honors)--College of William and Mary, 2009. / Includes bibliographical references (leaves 56-57). Also available via the World Wide Web.

Made available in DSpace on 2014-11-10T11:09:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-08-02Bitstream added on 2014-11-10T11:57:46Z : No. of bitstreams: 1 000788290.pdf: 1350300 bytes, checksum: efc63ae2b101504d42d2745bc5a4a3c9 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho estudaremos a aproximaçãoo de equações diferenciais parabólicas semilineares através de sua discretização via o método de elementos finitos. Vamos provar que os atratores da discretizaçãoao se comportam continuamente quando o tamanho do passo tende a zero estendendo os resultados de [17]. Vamos também calcular a taxa de convergência dos atratores em termos do passo da discretização / In this work we study the approximation of semilinear parabolic di erential equations through their discretization via the nite element method. We prove that the attractors of discretization behave continuously when the step size tends to zero extending the results of [17]. We also calculate the rate of convergence of attractors in terms of step of discretization

Nesse trabalho apresentamos o estudo do artigo [25] que analisa a existência de atratores globais para uma classe de equações da onda amortecida da forma \'épsilon u IND. tt\' + \'alpha\' (x) u IND. t\' + \'BETA\' (x)u - \'\\SIGMA SOBRE i, j\' \'\\PARTIAL ind. I\' (\'a IND. i j\' (x) \'PARTIAL IND. j u\') = f(x, u) , x PERTENCE A ÔMEGA\'\', t \'PERTENCE A\' [0,\'infinito\'), u (x, t) = 0, x \'PERTENCE A\' \'\\PARTIAL ÔMEGA\', t \'PERTENCE A\' [0, \'infinito\') definidas em um domínio arbitrário \'ÔMEGA\' / In this work we describe the results of the paper [25]. In [25] the authors prove existence of global attractors for the following semilinear damped wave equation \'\\épsilon u IND. t\'t + \'alpha\'(x)u IND. t\' + \'beta\' (x)u - \'\\SIGMA SOBRE i, j \'\\PARTIAL IND. i\' (\'a IND. i j\' (x) \'\\PARTIAL IND. j u\') = f (x, u), x \'IT BELONGS\' \'ÔMEGA\', t \'IT BELONGS\' [0, \'INFINITY\'), u(x,t), x \'IT BELONGS\' \'\\PARTIAL ÔMEGA\', t \'IT BELONGS\' [), \'INFINITY\'0 on an arbitrary domain \'OMEGA\'

Submitted by Bruna Rodrigues (bruna92rodrigues@yahoo.com.br) on 2016-10-21T12:07:15Z No. of bitstreams: 1 DissTRSC.pdf: 1059064 bytes, checksum: e90e2f60e1b722ad60105cfcdea16cc8 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-11-08T18:53:04Z (GMT) No. of bitstreams: 1 DissTRSC.pdf: 1059064 bytes, checksum: e90e2f60e1b722ad60105cfcdea16cc8 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-11-08T18:53:11Z (GMT) No. of bitstreams: 1 DissTRSC.pdf: 1059064 bytes, checksum: e90e2f60e1b722ad60105cfcdea16cc8 (MD5) / Made available in DSpace on 2016-11-08T18:53:17Z (GMT). No. of bitstreams: 1 DissTRSC.pdf: 1059064 bytes, checksum: e90e2f60e1b722ad60105cfcdea16cc8 (MD5) Previous issue date: 2016-03-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / This work is about the upper semicontinuity of the family of global attractors associated to nonlinear reaction diffusion equations whose principal part is determined by maximal operator monotonous governed by degenerate p-Laplacian in which the diffusion d blows up in localized regions inside the domain. / Este trabalho é sobre a semicontinuidade superior de uma família de atratores globais associados a equações de reação-difusão, não-lineares, cujo termo principal é determinado por um operador maximal monótono governado pelo p-Laplaciano degenerado em que a difusão d explode em regiões localizadas dentro do domínio.

Orientador: German Jesus Lozada Cruz / Banca: Alexandre Nolasco de Carvalho / Banca: Luiz Augusto Fernandes de Oliveira / Banca: José Antonio Langa Rosado / Banca: Waldemar Donizete Bastos / Resumo: Neste trabalho estudaremos a aproximaçãoo de equações diferenciais parabólicas semilineares através de sua discretização via o método de elementos finitos. Vamos provar que os atratores da discretizaçãoao se comportam continuamente quando o tamanho do passo tende a zero estendendo os resultados de [17]. Vamos também calcular a taxa de convergência dos atratores em termos do passo da discretização / Abstract: In this work we study the approximation of semilinear parabolic di erential equations through their discretization via the nite element method. We prove that the attractors of discretization behave continuously when the step size tends to zero extending the results of [17]. We also calculate the rate of convergence of attractors in terms of step of discretization / Doutor

Made available in DSpace on 2015-04-20T12:33:49Z (GMT). No. of bitstreams: 1 Tese Kedma yamamoto final agosto 2011.pdf: 1602993 bytes, checksum: 84439325cb6d0fa680dee7acd14a9088 (MD5) Previous issue date: 2011-06-14 / FAPEAM - Fundação de Amparo à Pesquisa do Estado do Amazonas / Studies on the role of artificial reefs and related structures are quite widespread in the marine literature, however knowledge about its effects on the biota of inland waters is still incipient. A study was conducted in lakes National Park Anavilhanas, Manaus / Am, to analyze the effects of increasing heterogeneity through the use of artificial attractors on the fish assemblages and populations of piscivorous in open water habitat. We also tested the influence of the attractors in two fixed levels of environmental complexity and its relationship to biotic and abiotic factors. Samples were taken four lakes using batteries of different sizes of gillnets, in the morning and evening for twenty-four months. The results showed that the artificial attractors exert a strong influence on fish assemblages in dry seasons, the abundance and diversity respond related to this environmental change. The heterogeneity near the attractors not in the abundance and diversity of the assemblages. Analysis of variance with repeated measures indicated significant differences between attractor and control for the number of species and the Berger-Parker dominance, using as response variable numerical abundance and weight. The environmental variables indicated by significant regression on the diversity of piscivores pH, oxygen and temperature. The number of species of piscivores was higher than in control attractors. Cichlid populations occurred only in areas of the attractor and the period of drought. / Estudos sobre o papel de recifes artificiais e estruturas correlatas são bastante difundidas na literatura marinha, entretanto o conhecimento sobre seus efeitos na biota de águas interiores ainda é incipiente. A pesquisa foi desenvolvido em lagos do Parque Nacional de Anavilhanas, Manaus/Am, para analisar os efeitos do aumento da heterogeneidade ambiental através do uso de atratores artificiais, sobre a estrutura das assembléias de peixes e de populações de piscívoros em habitat de água aberta. Testamos também, a influência dos atratores fixados em dois níveis de complexidade ambiental e suas relações com fatores bióticos e abióticos. Foram realizadas coletas durante dois ciclos hidrológicos, em quatro lagos usando baterias de malhadeiras de diferentes tamanhos, com despescas pela manhã e à noite durante vinte e quatro meses. Os resultados revelaram que os atratores artificiais exercem forte influência sobre as assembléias de peixes nas estações secas, a abundância e a diversidade respondem de forma relacionada a esta mudança ambiental. A heterogeneidade ambiental próxima aos atratores não apresentou influência na diversidade e abundância das assembléias. A Análise de variância com medidas repetidas no tempo indicou haver diferenças significativas entre atrator e controle para o número de espécies e na dominância de Berger-Parker, usando como variável resposta a abundância numérica e peso. As variáveis ambientais significativas indicadas pela Regressão sobre a diversidade de piscívoros foram o pH, oxigênio e a temperatura. O número de espécies de piscívoros foi maior nos atratores do que no controle. Populações de ciclídeos ocorreram somente nas áreas de atrator e durante o período de seca.

Neste trabalho estudamos a continuidade da dinâmica assintótica relativamente a perturbações e, em particular, exploramos a obtenção de melhorias para as taxas de convergência de atratores globais através da introdução de fatores de correção, inspirados pelos resultados da teoria de homogeneização e nos trabalhos de (BABIN; VISHIK, 1992) e (CARVALHO; CHOLEWA, 2011), e através da introdução de mecanismos que melhoram a transferência da taxa de convergência de semigrupos para a taxa de convergência de atratores, inspirados pelos trabalhos (SANTAMARÍA, 2013) e (BABIN; VISHIK, 1992; CARVALHO; CHOLEWA, 2011). A proposta inicial está centrada na obtenção de melhores taxas de convergência de atratores globais através da obtenção de equiatração e da melhoria da taxa de convergência dos semigrupos. Para isto, buscamos melhorar a taxa de convergência do resolvente dos operadores setoriais envolvidos, por meio de uma perturbação singular do resolvente limite que ainda gere uma família de operadores setoriais com resolventes que aproximam o resolvente do problema limite e aproximam melhor os resolventes das perturbações iniciais. Feito isto, obtemos uma melhora imediata de convergência dos semigrupos lineares, depois dos não lineares (através da fórmula da variação das constantes). Motivados pelos resultados de (SANTAMARÍA, 2013), que oferecem uma menor perda na transferência das taxas de convergência dos semigrupos para as taxas de convergência dos atratores, buscamos melhor compreender a propriedade Lipschitz Shadowing, que é responsável direta pela obtenção da taxa de convergência dos atratores diretamente da taxa de convergência dos semigrupos. Isto nos levou a descobrir que podemos obter as propriedade Lipschitz Shadowing e estabilidade estrutural para perturbações Lipschitz de semigrupos Morse-Smale. / Here we compare the continuity of the asymptotic dynamics with respect to perturbations and, in particular, we explored to obtain improvement of rates of convergence of the global attractor through the introduction of correction factors, inspired by the results of homogenization theory and work of (BABIN; VISHIK, 1992) and (CARVALHO; CHOLEWA, 2011), and the introduction of mechanisms that improve the transference of the convergence rate of semigroups to the convergence rate of attractors, inspired by the work of (SANTAMARÍA, 2013) and (BABIN; VISHIK, 1992; CARVALHO; CHOLEWA, 2011). The initial proposal is focused on achieving best rates of convergence of the global attractors by obtaining equi-atraction and improving the convergence rate of semigroups. For this, we seek to improve the rate of convergence of the resolvents of sectorial operators, through a singular perturbation of the resolvent associated with the limit problem and generate a new family of sectorial operators whose resolvents both approximate the resolvent of the limit problem as they were closer to the resolvents the initial perturbation. Having done this, we obtain an immediate improvement of convergence of linear semigroups, after the non-linear (using the variation of constants formula). Motivated by the results of (SANTAMARÍA, 2013), which offer an improvement in obtaining convergence rates, we seek to study property better Lipschitz Shadowing, which is basically responsible for obtaining the distance of the attractors directly from the convergence rate of the semigroups. This has led us to discover that we can both preserve the Lipschitz Shadowing property under Lipschitz perturbations of Morse-Smale semigroups, and The geometric stability of the attractors.