ABUNDANCE OF CHAOS IN ONE-DIMENSIONAL POPULATION DYNAMICS

Equadiff 99 ◽  
2000 ◽  
pp. 1229-1231
Author(s):  
HANS THUNBERG
Keyword(s):  
Population Dynamics ◽  
One Dimensional

POPULATION DYNAMICS IN HETEROGENEOUS ENVIRONMENTS: A DISCRETE MODEL

2000 ◽  
Vol 10 (08) ◽  
pp. 1993-2000 ◽  
Author(s):  
BASTIEN FERNANDEZ ◽  
VALERY TERESHKO
Keyword(s):  
Population Dynamics ◽  
Periodic Orbit ◽  
Discrete Model ◽  
Mean Field ◽  
Heterogeneous Environments ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Population Spread ◽  
Asymptotic Dynamics ◽  
Time Periodic

We study the dynamics of a multidimensional coordinate-dependent mapping governing the time evolution of a population spread over a one-dimensional lattice. The nonlinearity is of mean-field type and the dependence on coordinates, given by the so-called fitness, allows to take into account the spatial heterogeneities of the habitat. A global picture of the dynamics is given in the case without diffusion and in the case with diffusion when the fitness is homogeneous and leads to a periodic orbit. Moreover it is shown that, periodic fitnesses close to homogeneous ones impose their periodicity on the asymptotic dynamics when the latter is time-periodic.

scholarly journals One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics

2021 ◽  
Vol 175 (1) ◽  
Author(s):  
Eugenia Franco ◽  
Mats Gyllenberg ◽  
Odo Diekmann
Keyword(s):  
Mathematical Biology ◽  
Population Dynamics ◽  
Asymptotic Behaviour ◽  
Dimensional Reduction ◽  
Large Time ◽  
Renewal Equation ◽  
Time Behaviour ◽  
Renewal Theorem ◽  
One Dimensional ◽  
Renewal Equations

AbstractDespite their relevance in mathematical biology, there are, as yet, few general results about the asymptotic behaviour of measure valued solutions of renewal equations on the basis of assumptions concerning the kernel. We characterise, via their kernels, a class of renewal equations whose measure-valued solution can be expressed in terms of the solution of a scalar renewal equation. The asymptotic behaviour of the solution of the scalar renewal equation, is studied via Feller’s classical renewal theorem and, from it, the large time behaviour of the solution of the original renewal equation is derived.

Numerical Solution of Diffusion and Reaction–Diffusion Partial Integro-Differential Equations

2018 ◽  
Vol 15 (06) ◽  
pp. 1850047 ◽  
Author(s):  
Imran Aziz ◽  
Imran Khan
Keyword(s):  
Population Dynamics ◽  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Method ◽  
Reaction Diffusion ◽  
Nonlinear Problems ◽  
Haar Wavelet ◽  
Benchmark Problems ◽  
Two Dimensional ◽  
One Dimensional

In this paper, a collocation method based on Haar wavelet is developed for numerical solution of diffusion and reaction–diffusion partial integro-differential equations. The equations are parabolic partial integro-differential equations and we consider both one-dimensional and two-dimensional cases. Such equations have applications in several practical problems including population dynamics. An important advantage of the proposed method is that it can be applied to both linear as well as nonlinear problems with slide modification. The proposed numerical method is validated by applying it to various benchmark problems from the existing literature. The numerical results confirm the accuracy, efficiency and robustness of the proposed method.

Numerical simulation of the one-dimensional population dynamics with nonlocal competitive losses and convection

2011 ◽  
Vol 54 (4) ◽  
pp. 479-484 ◽  
Author(s):  
V. A. Aleutdinova ◽  
A. V. Borisov ◽  
V. É. Shaparev ◽  
A. V. Shapovalov
Keyword(s):  
Numerical Simulation ◽  
Population Dynamics ◽  
One Dimensional ◽  
The One

scholarly journals Analytical investigation of the onset of bifurcation cascade in two logistic-like maps

2001 ◽  
Vol 6 (1) ◽  
pp. 31-35
Author(s):  
S. Panchev
Keyword(s):  
Population Dynamics ◽  
Analytical Study ◽  
Logistic Map ◽  
Period Doubling ◽  
Analytical Investigation ◽  
Dynamics Modeling ◽  
One Dimensional ◽  
Basic Model

Two modifications of the classical one-dimensional logistic map are proposed, which permitted analytical study of the onset of the bifurcation (period doubling) cascade. The modified maps are two-parametric ones. This introduces new features in their behaviour and makes them more flexible. The results can prove to be useful in the ecological (population dynamics) modeling, where the logistic map is a basic model and also in other fields of application.

DRESSED EXCITONS IN MICROCAVITY

1995 ◽  
Vol 04 (01) ◽  
pp. 13-25 ◽  
Author(s):  
E. HANAMURA ◽  
J. INOUE ◽  
F. YURA
Keyword(s):  
Population Dynamics ◽  
Emission Spectrum ◽  
Nonlinear Optical ◽  
Single Mode ◽  
Quantum Mechanical ◽  
Radiation Mode ◽  
Rabi Splitting ◽  
One Dimensional ◽  
Optical Responses ◽  
Vacuum Rabi Splitting

After reviewing the important roles of excitons in nonlinear optical responses, we demonstrate mutual and quantum-mechanical control of radiation field and excitons on the same footing in a microcavity. First we introduce dressed excitons as bosons interacting coherently and reversibly with a radiation mode in the microcavity. Although the vacuum Rabi splitting of the dressed exciton is the same as that of dressed atom, the emission spectrum under strong pumping shows quartet structure different from the triplet of dressed atom. Secondly, the population dynamics of dressed excitons, i.e., one-dimensional polaritons in the mesoscopic system is solved and the dominant distribution on a single mode is demonstrated above the critical pumping.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

1970 ◽  
Vol 28 ◽  
pp. 478-479
Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi
Keyword(s):  
Surface Layer ◽  
Electric Fields ◽  
Quantitative Study ◽  
Recent Progress ◽  
Ferroelectric Domain ◽  
Resolving Power ◽  
Surface Pattern ◽  
Crystal Surfaces ◽  
One Dimensional ◽  
Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

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