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Papers by Jacques Douglas Silva

Research paper thumbnail of Asymptotic transversal stability for synchronized attractors in a metapopulation model

Mathematical Methods in the Applied Sciences, 2015

ABSTRACT

Research paper thumbnail of Migração e Sincronismo em certos Modelos Populacionais

TEMA - Tendências em Matemática Aplicada e Computacional, 2006

Resumo. Neste trabalho obtemos condições suficientes para a estabilidade daś orbitas sincronizada... more Resumo. Neste trabalho obtemos condições suficientes para a estabilidade daś orbitas sincronizadas de sistemas dinâmicos acoplados provenientes de modelos populacionais com a migração dependente da densidade.

Research paper thumbnail of An Age-Dependent Metapopulation Model

Mathematics in Industry, 2010

A dynamic model of a network of coupled populations is developed. In each of the n sites in the n... more A dynamic model of a network of coupled populations is developed. In each of the n sites in the network a local demographic model of Leslie type is used. Connection between locations is modeled through density-independent migration which is a function of age and also on the connecting sites. We perform a simulation illustrating a policy of reduction of excessive migration.

Research paper thumbnail of Stability of Traveling Waves in Quasi-Linear Hyperbolic Systems with Relaxation and Diffusion

SIAM Journal on Mathematical Analysis, 2008

ABSTRACT We establish the existence and the stability of traveling wave solutions of a quasilinea... more ABSTRACT We establish the existence and the stability of traveling wave solutions of a quasilinear hyperbolic system with both relaxation and diffusion. The traveling wave solutions are shown to be asymptotically stable under small disturbances and under the subcharacteristic condition using a weighted energy method. The delicate balance between the relaxation and the diffusion that leads to the stability of the traveling waves is identified; namely, the diffusion coefficient is bounded by a constant multiple of the relaxation time. Such a result provides an important first step toward the understanding of the transition from stability to instability as parameters vary in physical problems involving both relaxation and diffusion.

Research paper thumbnail of Synchronism in population networks with non linear coupling

Nonlinear Analysis: Real World Applications, 2010

A quite general spatially explicit metapopulation model featuring density-dependent dispersal is ... more A quite general spatially explicit metapopulation model featuring density-dependent dispersal is proposed. A study of the stability of synchronized attractors is done based on an explicit calculation of the transverse Lyapunov number of these attractors. An analytic expression for the transverse Lyapunov number depending on the Lyapunov number of the synchronous trajectory, the eigenvalues of the network configuration matrix and the function modelling the density-dependent dispersal (the number of migrants as a function of the local density) is presented. Numerical simulations are also performed upon selecting biologically relevant features, such as local dynamics, network topology and density-dependent dispersal mechanism.

Research paper thumbnail of Density-dependent dispersal in multiple species metapopulations

Mathematical Biosciences and Engineering, 2008

A multiple species metapopulations model with density-dependent dispersal is presented. Assuming ... more A multiple species metapopulations model with density-dependent dispersal is presented. Assuming the network configuration matrix to be diagonizable we obtain a decoupling of the associated perturbed system from the homogeneous state. It was possible to analyze in detail the instability induced by the density-dependent dispersal in two classes of k-species interaction models: a hierarchically organized competitive system and an age-structured model.

Research paper thumbnail of Population distribution and synchronized dynamics in a metapopulation model in two geographic scales

Mathematical Biosciences, 2014

In this paper, a metapopulation model composed of patches distributed in two spatial scales is pr... more In this paper, a metapopulation model composed of patches distributed in two spatial scales is proposed in order to study the stability of synchronous dynamics. Clusters of patches connected by short-range dispersal are assumed to be formed. Long distance dispersal is responsible to link patches that are in different clusters. During each time step, we assume that there are three processes involved in the population dynamics: (a) the local dynamics, which consists of reproduction and survival; (b) short-range dispersal of individuals between the patches of each cluster; and (c) the movement between the clusters. First we present an analytic criterion for regional synchronization, where the clusters evolve with the same dynamics. We then discuss the possibility of a full synchronism, where all patches in the network follow the same time evolution. The existence of such a state is not always ensured, even considering that all patches have the same local dynamics. It depends on how the individuals are distributed among the local patches that compose a cluster after long-range dispersal takes place in the regional scale. An analytic criterion for the stability of synchronized trajectories in this case is obtained.

Research paper thumbnail of Reproductive schedules in a density-dependent recruitment model

Mathematical Biosciences, 1997

Understanding the mechanisms that regulate stability and oscillatroy behavior requires isolated s... more Understanding the mechanisms that regulate stability and oscillatroy behavior requires isolated studies of each of the mechanisms so that their effects can be recognized and measured when they are coupled in a system. The role of the shape of the reproductive schedule, including its time lag, in determining stability properties in an age-structured density-dependent recruitment continuous model is investigated. The results are independent of the strength of the density dependence. Under the assumption of rather simple reproductive schedules, explicit and implicit reproductive delays were found to have a destabilizing effect, whereas spreading the reproductive effort over larger intervals has a stabilizing effect. Moreover, the stability is determined solely by the interplay of the reproductive effort and by the ratio between the standard deviation of the maternity distribution and the mean age of reproduction. This ratio has a stabilizing effect.

Research paper thumbnail of Compensation and stability in nonlinear matrix models

Mathematical Biosciences, 1992

Stability, bifurcation, and dynamic behavior, investigated here in discrete, nonlinear, age-struc... more Stability, bifurcation, and dynamic behavior, investigated here in discrete, nonlinear, age-structured models, can be complex; however, restrictions imposed by compensatory mechanisms can limit the behavioral spectrum of a dynamic system. These limitations in transitional behavior of compensatory models are a focal point of this article. Although there is a tendency for compensatory models to be stable, we demonstrate that stability in compensatory systems does not always occur; for example, equilibria arising through a bifurcation can be initially unstable. Results concerning existence and uniqueness of equilibria, stability of the equilibria, and boundedness of solutions suggest that "compensatory" systems might not be compensatory in the literal sense.

Research paper thumbnail of Stability in an age-structured metapopulation model

Journal of Mathematical Biology, 2005

We present a discrete model for a metapopulation of a single species with overlapping generations... more We present a discrete model for a metapopulation of a single species with overlapping generations. Based on the dynamical behavior of the system in absence of dispersal, we have shown that a migration mechanism which depends only on age can not stabilize a previously unstable homogeneous equilibrium, but can drive a stable uncoupled system to instability if the migration rules are strongly related to age structure.

Research paper thumbnail of Stability in a Metapopulation Model with Density-dependent Dispersal

Bulletin of Mathematical Biology, 2001

A spatially explicit metapopulation model with positive density-dependent migration is analysed. ... more A spatially explicit metapopulation model with positive density-dependent migration is analysed. We obtained conditions under which a previously stable system can be driven to instability caused by a density-dependent migration mechanism. The stability boundary depends on the rate of increase of the number of migrants on each site at local equilibrium, on the intrinsic rate of increase at local level, on the number of patches, and on topological aspects regarding the connectivity between patches. A concrete example is presented illustrating the dynamics on the dispersal-induced unstable regime.

Research paper thumbnail of Synchronism in a Metapopulation Model

Bulletin of Mathematical Biology, 2000

Research paper thumbnail of Density-dependent migration and synchronism in metapopulations

Bulletin of Mathematical Biology, 2006

A spatially explicit metapopulation model with density-dependent dispersal is proposed in order t... more A spatially explicit metapopulation model with density-dependent dispersal is proposed in order to study the stability of synchronous dynamics. A stability criterion is obtained based on the computation of the transversal Liapunov number of attractors on the synchronous invariant manifold. We examine in detail a special case of density-dependent dispersal rule where migration does not occur if the patch density is below a certain critical density, while the fraction of individuals that migrate to other patches is kept constant if the patch density is above the threshold level. Comparisons with density-independent migration models indicate that this simple density-dependent dispersal mechanism reduces the stability of synchronous dynamics. We were able to quantify exactly this loss of stability through the frequency that synchronous trajectories are above the critical density.

Research paper thumbnail of Asymptotic transversal stability for synchronized attractors in a metapopulation model

Mathematical Methods in the Applied Sciences, 2015

ABSTRACT

Research paper thumbnail of Migração e Sincronismo em certos Modelos Populacionais

TEMA - Tendências em Matemática Aplicada e Computacional, 2006

Resumo. Neste trabalho obtemos condições suficientes para a estabilidade daś orbitas sincronizada... more Resumo. Neste trabalho obtemos condições suficientes para a estabilidade daś orbitas sincronizadas de sistemas dinâmicos acoplados provenientes de modelos populacionais com a migração dependente da densidade.

Research paper thumbnail of An Age-Dependent Metapopulation Model

Mathematics in Industry, 2010

A dynamic model of a network of coupled populations is developed. In each of the n sites in the n... more A dynamic model of a network of coupled populations is developed. In each of the n sites in the network a local demographic model of Leslie type is used. Connection between locations is modeled through density-independent migration which is a function of age and also on the connecting sites. We perform a simulation illustrating a policy of reduction of excessive migration.

Research paper thumbnail of Stability of Traveling Waves in Quasi-Linear Hyperbolic Systems with Relaxation and Diffusion

SIAM Journal on Mathematical Analysis, 2008

ABSTRACT We establish the existence and the stability of traveling wave solutions of a quasilinea... more ABSTRACT We establish the existence and the stability of traveling wave solutions of a quasilinear hyperbolic system with both relaxation and diffusion. The traveling wave solutions are shown to be asymptotically stable under small disturbances and under the subcharacteristic condition using a weighted energy method. The delicate balance between the relaxation and the diffusion that leads to the stability of the traveling waves is identified; namely, the diffusion coefficient is bounded by a constant multiple of the relaxation time. Such a result provides an important first step toward the understanding of the transition from stability to instability as parameters vary in physical problems involving both relaxation and diffusion.

Research paper thumbnail of Synchronism in population networks with non linear coupling

Nonlinear Analysis: Real World Applications, 2010

A quite general spatially explicit metapopulation model featuring density-dependent dispersal is ... more A quite general spatially explicit metapopulation model featuring density-dependent dispersal is proposed. A study of the stability of synchronized attractors is done based on an explicit calculation of the transverse Lyapunov number of these attractors. An analytic expression for the transverse Lyapunov number depending on the Lyapunov number of the synchronous trajectory, the eigenvalues of the network configuration matrix and the function modelling the density-dependent dispersal (the number of migrants as a function of the local density) is presented. Numerical simulations are also performed upon selecting biologically relevant features, such as local dynamics, network topology and density-dependent dispersal mechanism.

Research paper thumbnail of Density-dependent dispersal in multiple species metapopulations

Mathematical Biosciences and Engineering, 2008

A multiple species metapopulations model with density-dependent dispersal is presented. Assuming ... more A multiple species metapopulations model with density-dependent dispersal is presented. Assuming the network configuration matrix to be diagonizable we obtain a decoupling of the associated perturbed system from the homogeneous state. It was possible to analyze in detail the instability induced by the density-dependent dispersal in two classes of k-species interaction models: a hierarchically organized competitive system and an age-structured model.

Research paper thumbnail of Population distribution and synchronized dynamics in a metapopulation model in two geographic scales

Mathematical Biosciences, 2014

In this paper, a metapopulation model composed of patches distributed in two spatial scales is pr... more In this paper, a metapopulation model composed of patches distributed in two spatial scales is proposed in order to study the stability of synchronous dynamics. Clusters of patches connected by short-range dispersal are assumed to be formed. Long distance dispersal is responsible to link patches that are in different clusters. During each time step, we assume that there are three processes involved in the population dynamics: (a) the local dynamics, which consists of reproduction and survival; (b) short-range dispersal of individuals between the patches of each cluster; and (c) the movement between the clusters. First we present an analytic criterion for regional synchronization, where the clusters evolve with the same dynamics. We then discuss the possibility of a full synchronism, where all patches in the network follow the same time evolution. The existence of such a state is not always ensured, even considering that all patches have the same local dynamics. It depends on how the individuals are distributed among the local patches that compose a cluster after long-range dispersal takes place in the regional scale. An analytic criterion for the stability of synchronized trajectories in this case is obtained.

Research paper thumbnail of Reproductive schedules in a density-dependent recruitment model

Mathematical Biosciences, 1997

Understanding the mechanisms that regulate stability and oscillatroy behavior requires isolated s... more Understanding the mechanisms that regulate stability and oscillatroy behavior requires isolated studies of each of the mechanisms so that their effects can be recognized and measured when they are coupled in a system. The role of the shape of the reproductive schedule, including its time lag, in determining stability properties in an age-structured density-dependent recruitment continuous model is investigated. The results are independent of the strength of the density dependence. Under the assumption of rather simple reproductive schedules, explicit and implicit reproductive delays were found to have a destabilizing effect, whereas spreading the reproductive effort over larger intervals has a stabilizing effect. Moreover, the stability is determined solely by the interplay of the reproductive effort and by the ratio between the standard deviation of the maternity distribution and the mean age of reproduction. This ratio has a stabilizing effect.

Research paper thumbnail of Compensation and stability in nonlinear matrix models

Mathematical Biosciences, 1992

Stability, bifurcation, and dynamic behavior, investigated here in discrete, nonlinear, age-struc... more Stability, bifurcation, and dynamic behavior, investigated here in discrete, nonlinear, age-structured models, can be complex; however, restrictions imposed by compensatory mechanisms can limit the behavioral spectrum of a dynamic system. These limitations in transitional behavior of compensatory models are a focal point of this article. Although there is a tendency for compensatory models to be stable, we demonstrate that stability in compensatory systems does not always occur; for example, equilibria arising through a bifurcation can be initially unstable. Results concerning existence and uniqueness of equilibria, stability of the equilibria, and boundedness of solutions suggest that "compensatory" systems might not be compensatory in the literal sense.

Research paper thumbnail of Stability in an age-structured metapopulation model

Journal of Mathematical Biology, 2005

We present a discrete model for a metapopulation of a single species with overlapping generations... more We present a discrete model for a metapopulation of a single species with overlapping generations. Based on the dynamical behavior of the system in absence of dispersal, we have shown that a migration mechanism which depends only on age can not stabilize a previously unstable homogeneous equilibrium, but can drive a stable uncoupled system to instability if the migration rules are strongly related to age structure.

Research paper thumbnail of Stability in a Metapopulation Model with Density-dependent Dispersal

Bulletin of Mathematical Biology, 2001

A spatially explicit metapopulation model with positive density-dependent migration is analysed. ... more A spatially explicit metapopulation model with positive density-dependent migration is analysed. We obtained conditions under which a previously stable system can be driven to instability caused by a density-dependent migration mechanism. The stability boundary depends on the rate of increase of the number of migrants on each site at local equilibrium, on the intrinsic rate of increase at local level, on the number of patches, and on topological aspects regarding the connectivity between patches. A concrete example is presented illustrating the dynamics on the dispersal-induced unstable regime.

Research paper thumbnail of Synchronism in a Metapopulation Model

Bulletin of Mathematical Biology, 2000

Research paper thumbnail of Density-dependent migration and synchronism in metapopulations

Bulletin of Mathematical Biology, 2006

A spatially explicit metapopulation model with density-dependent dispersal is proposed in order t... more A spatially explicit metapopulation model with density-dependent dispersal is proposed in order to study the stability of synchronous dynamics. A stability criterion is obtained based on the computation of the transversal Liapunov number of attractors on the synchronous invariant manifold. We examine in detail a special case of density-dependent dispersal rule where migration does not occur if the patch density is below a certain critical density, while the fraction of individuals that migrate to other patches is kept constant if the patch density is above the threshold level. Comparisons with density-independent migration models indicate that this simple density-dependent dispersal mechanism reduces the stability of synchronous dynamics. We were able to quantify exactly this loss of stability through the frequency that synchronous trajectories are above the critical density.