7,841 research outputs found
Physiologically structured populations with diffusion and dynamic boundary conditions
We consider a linear size-structured population model with diffusion in the
size-space. Individuals are recruited into the population at arbitrary sizes.
The model is equipped with generalized Wentzell-Robin (or dynamic) boundary
conditions. This allows modelling of "adhesion" at extremely small or large
sizes. We establish existence and positivity of solutions by showing that
solutions are governed by a positive quasicontractive semigroup of linear
operators on the biologically relevant state space. This is carried out via
establishing dissipativity of a suitably perturbed semigroup generator. We also
show that solutions of the model exhibit balanced exponential growth, that is
our model admits a finite dimensional global attractor. In case of strictly
positive fertility we are able to establish that solutions in fact exhibit
asynchronous exponential growth
Steady states in hierarchical structured populations with distributed states at birth
We investigate steady states of a quasilinear first order hyperbolic partial
integro-differential equation. The model describes the evolution of a
hierarchical structured population with distributed states at birth.
Hierarchical size-structured models describe the dynamics of populations when
individuals experience size-specific environment. This is the case for example
in a population where individuals exhibit cannibalistic behavior and the chance
to become prey (or to attack) depends on the individual's size. The other
distinctive feature of the model is that individuals are recruited into the
population at arbitrary size. This amounts to an infinite rank integral
operator describing the recruitment process. First we establish conditions for
the existence of a positive steady state of the model. Our method uses a fixed
point result of nonlinear maps in conical shells of Banach spaces. Then we
study stability properties of steady states for the special case of a separable
growth rate using results from the theory of positive operators on Banach
lattices.Comment: to appear in Discrete and Continuous Dynamical Systems - Series
Size-structured populations: immigration, (bi)stability and the net growth rate
We consider a class of physiologically structured population models, a first
order nonlinear partial differential equation equipped with a nonlocal boundary
condition, with a constant external inflow of individuals. We prove that the
linearised system is governed by a quasicontraction semigroup. We also
establish that linear stability of equilibrium solutions is governed by a
generalized net reproduction function. In a special case of the model
ingredients we discuss the nonlinear dynamics of the system when the spectral
bound of the linearised operator equals zero, i.e. when linearisation does not
decide stability. This allows us to demonstrate, through a concrete example,
how immigration might be beneficial to the population. In particular, we show
that from a nonlinearly unstable positive equilibrium a linearly stable and
unstable pair of equilibria bifurcates. In fact, the linearised system exhibits
bistability, for a certain range of values of the external inflow, induced
potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin
Spatial flocking: Control by speed, distance, noise and delay
Fish, birds, insects and robots frequently swim or fly in groups. During
their 3 dimensional collective motion, these agents do not stop, they avoid
collisions by strong short-range repulsion, and achieve group cohesion by weak
long-range attraction. In a minimal model that is isotropic, and continuous in
both space and time, we demonstrate that (i) adjusting speed to a preferred
value, combined with (ii) radial repulsion and an (iii) effective long-range
attraction are sufficient for the stable ordering of autonomously moving agents
in space. Our results imply that beyond these three rules ordering in space
requires no further rules, for example, explicit velocity alignment, anisotropy
of the interactions or the frequent reversal of the direction of motion,
friction, elastic interactions, sticky surfaces, a viscous medium, or vertical
separation that prefers interactions within horizontal layers. Noise and delays
are inherent to the communication and decisions of all moving agents. Thus,
next we investigate their effects on ordering in the model. First, we find that
the amount of noise necessary for preventing the ordering of agents is not
sufficient for destroying order. In other words, for realistic noise amplitudes
the transition between order and disorder is rapid. Second, we demonstrate that
ordering is more sensitive to displacements caused by delayed interactions than
to uncorrelated noise (random errors). Third, we find that with changing
interaction delays the ordered state disappears at roughly the same rate,
whereas it emerges with different rates. In summary, we find that the model
discussed here is simple enough to allow a fair understanding of the modeled
phenomena, yet sufficiently detailed for the description and management of
large flocks with noisy and delayed interactions. Our code is available at
http://github.com/fij/flocComment: 12 pages, 7 figure
Semigroup analysis of structured parasite populations
Motivated by structured parasite populations in aquaculture we consider a
class of size-structured population models, where individuals may be recruited
into the population with distributed states at birth. The mathematical model
which describes the evolution of such a population is a first-order nonlinear
partial integro-differential equation of hyperbolic type. First, we use
positive perturbation arguments and utilise results from the spectral theory of
semigroups to establish conditions for the existence of a positive equilibrium
solution of our model. Then, we formulate conditions that guarantee that the
linearised system is governed by a positive quasicontraction semigroup on the
biologically relevant state space. We also show that the governing linear
semigroup is eventually compact, hence growth properties of the semigroup are
determined by the spectrum of its generator. In the case of a separable
fertility function, we deduce a characteristic equation, and investigate the
stability of equilibrium solutions in the general case using positive
perturbation arguments.Comment: to appear in Mathematical Modelling of Natural Phenomen
Bibliography and checklist of foliicolous lichenized fungi up to 1992
Bibliographic records are presented of 324 scientific papers on foliicolous lichenized fungi published subsequent to Santesson’s survey of 1952. The 482 species presently known are listed in an alphabetical checklist, with references to important descriptions, keys and illustrations published by or after Santesson (1952), and an indication of the distribution. Also added are all synonyms used after 1952. Introductory chapters deal with the present state of research on foliicolous lichens and its history. The following new combination is proposed: Strigula smaragdula Fr. var. stellata (Nyl. & Cromb.) Farkas
Connectivity-Based Self-Localization in WSNs
Efficient localization methods are among the major challenges in wireless sensor networks today. In this paper, we present our so-called connectivity based approach i.e, based on local connectivity information, to tackle this problem. At first the method fragments the network into larger groups labeled as packs. Based on the mutual connectivity relations with their surrounding packs, we identify border nodes as well as the central node. As this first approach requires some a-priori knowledge on the network topology, we also present a novel segment-based fragmentation method to estimate the central pack of the network as well as detecting so-called corner packs without any a-priori knowledge. Based on these detected points, the network is fragmented into a set of even larger elements, so-called segments built on top of the packs, supporting even more localization information as they all reach the central node
Analysis of Minimal LDPC Decoder System on a Chip Implementation
This paper presents a practical method of potential replacement of several different Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes with one, with the intention of saving as much memory as required to implement the LDPC encoder and decoder in a memory-constrained System on a Chip (SoC). The presented method requires only a very small modification of the existing encoder and decoder, making it suitable for utilization in a Software Defined Radio (SDR) platform. Besides the analysis of the effects of necessary variable-node value fixation during the Belief Propagation (BP) decoding algorithm, practical standard-defined code parameters are scrutinized in order to evaluate the feasibility of the proposed LDPC setup simplification. Finally, the error performance of the modified system structure is evaluated and compared with the original system structure by means of simulation
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