Coexistence Of Solutions Research Articles

Algal competition in a water column with excessive dioxide in the atmosphere.

This paper deals with a resource competition model of two algal species in a water column with excessive dioxide in the atmosphere. First, the uniqueness of positive steady state solutions to the single-species model with two resources is established by the application of the degree theory and the strong maximum principle for the cooperative system. Second, some asymptotic behavior of the single-species model is given by comparison principle and uniform persistence theory. Third, the coexistence solutions to the competition system of two species with two substitutable resources are obtained by global bifurcation theory, various estimates and the strong maximum principle for the cooperative system. Numerical simulations are used to illustrate the outcomes of coexistence and competitive exclusion.

Coexistence solutions of a competition model with two species in a water column

Competition between species for resources is a fundamental ecological process,which can be modeled by the mathematical models in the chemostat culture or in the water column. The chemostat-type models for resource competition have been extensively analyzed. However, the study on the competition for resources in the water column has been relatively neglected as a result of some technical difficulties.We consider a resource competition model with two species in the water column. Firstly, the global existenceand $L^\infty$ boundedness of solutions to the model are established by inequality estimates. Secondly, the uniqueness ofpositive steady state solutions and some dynamical behavior of the single population model are attained by degree theory and uniformpersistence theory. Finally, the structure of the coexistence solutions of the two-species system is investigated bythe global bifurcation theory.

A reaction–advection–diffusion system modeling the competition for two complementary resources with seasonality in a flowing habitat

In this current paper, we investigate a periodic bio-reactor model where microorganisms compete for two essential nutrient resource(s) needed for growth. For the single population growth model: we show that when the trivial solution is (locally) asymptotically stable, then the single population will be washed out; when the trivial solution is unstable, there is a unique periodic positive solution which attracts all solutions with nonzero initial data. For the two species model, we prove that the existence of a periodic coexistence state is possible if each species can invade the semi-trivial periodic state established by the other species. More precisely, if the semi-trivial periodic solutions are both unstable, there exists at least one periodic coexistence solution. Numerical work indicates conditions for persistence depend on the flow characteristics (advection and diffusivity). From our numerical simulations, competitive exclusion, bistability, and coexistence are all observed.

Interkulturalni odgoj i obrazovanje kao čimbenik suživota u multikulturalnom društvu

Susreti različitih kultura u suvremenom svijetu zbivaju se gotovo svakog trena u najraznovrsnijim oblicima komuniciranja. Razvoj odnosa prema kulturno drugačijima postaje ključnim čimbenikom suočavanja s neminovnim promjenama uzrokovanima prijelazom jedinstvenih monokulturalnih u kulturno-pluralne zajednice. Međusobni kontakti pripadnika različitih kultura pritom podrazumijevaju nužnost kvalitetnog suodnosa temeljenog na ideji interkulturalizma koji se javlja kao moguće rješenje za kvalitetan suživot u multikulturalnom društvu. Suočene s posljedicama masovnih migracija na globalnoj razini, odgojno-obrazovne institucije postaju stjecištima različitih etniciteta, kultura, jezika, religija i svjetonazora, uslijed čega se javlja potreba ugradnje interkulturalnih načela u odgojno-obrazovne sustave europskih zemalja. Interkulturalni odgoj i obrazovanje, promatran u kontekstu promicanja europskih vrijednosti i podupiranja europske dimenzije obrazovanja kao dominantne smjernice obrazovnih politika europskih zemalja, implicira potrebu novog pristupa izradi kurikula, dok razvijanje interkulturalne kompetencije učitelja kao moderatora interkulturalnih odnosa predstavlja značajnu sastavnicu njihova cjeloživotnog obrazovanja prilagođenog potrebama i zahtjevima suvremenog multikulturalnog društva.

Theoretical Study of Interplay Between Superconductivity and Itinerant Ferromagnetism

Following Green’s function technique and equation of motion method, the coexistence of superconductivity (SC) and itinerant ferromagnetism (FM) is investigated in a single band homogenous system. Self consistent equations for SC and FM order parameters, Δ and m or I respectively are derived. It is shown that there generally exists a coexistent (Δ ≠ 0, and m or I ≠ 0) solutions to the coupled equations of the order parameter in the,temperature range 0 < T < min(TC, TFM), where TC and TFM are respectively the superconducting and ferromagnetic transition temperatures. Expressions for specific heat, density of states, free energy and critical field are derived. The specific heat has linear temperature dependence as opposed to the exponential decrease in the bCS theory. The density of states for a finite m increases as opposed to that of a ferromagnetic metal. Free energy study reveals that FM-SC state has lowest energy than the normal FM state and therefore realized at low enough temperature .Effect of small external field is also studied. The theory is applied to explain the observations in uranium based intermetallics systems UCoGe and UIr. The agreement between theory and experiments is quite encouraging.

Reconfigurable cognitive transceiver for opportunistic networks

In this work, we provide the implementation and analysis of a cognitive transceiver for opportunistic networks. We focus on a previously introduced dynamic spectrum access (DSA) - cognitive radio (CR) solution for primary-secondary coexistence in opportunistic orthogonal frequency division multiplexing (OFDM) networks, called cognitive interference alignment (CIA). The implementation is based on software-defined radio (SDR) and uses GNU Radio and the universal software radio peripheral (USRP) as the implementation toolkit. The proposed flexible transceiver architecture allows efficient on-the-fly reconfigurations of the physical layer into OFDM, CIA or a combination of both. Remarkably, its responsiveness is such that the uplink and downlink channel reciprocity from the medium perspective, inherent to time division duplex (TDD) communications, can be effectively verified and exploited. We show that CIA provides approximately 10 dB of interference isolation towards the OFDM receiver with respect to a fully random precoder. This result is obtained under suboptimal conditions, which indicates that further gains are possible with a better optimization of the system. Our findings point towards the usefulness of a practical CIA implementation, as it yields a non-negligible performance for the secondary system, while providing interference shielding to the primary receiver.

Coexistence solutions and their stability of an unstirred chemostat model with toxins

We study a reaction–diffusion system of the unstirred chemostat model with toxins in the N-dimensional case. Firstly, some sufficient conditions for the existence of positive steady-state solutions are obtained by means of the fixed point index theory. Secondly, the local structure of positive steady-state solutions and their stability are discussed by the bifurcation theory. Lastly, the effect of the toxins is investigated by the perturbation technique. The results show that when the parameter β, which measures the effect of toxins, is large enough, this model has no coexistence solution provided that the maximal growth rate b of the species v is greater than σˆ11−k, and all positive solutions of this model are controlled by a limit system provided that b belongs to the interval (σ11−k,σˆ11−k).

Multiple coexistence solutions to the unstirred chemostat model with plasmid and toxin

We investigate the effects of toxins on the multiple coexistence solutions of an unstirred chemostat model of competition between plasmid-bearing and plasmid-free organisms when the plasmid-bearing organism produces toxins. It turns out that coexistence solutions to this model are governed by two limiting systems. Based on the analysis of uniqueness and stability of positive solutions to two limiting systems, the exact multiplicity and stability of coexistence solutions of this model are established by means of the combination of the fixed-point index theory, bifurcation theory and perturbation theory.

The impact of predation on the coexistence and competitive exclusion of pathogens in prey

A two-strain epidemic model with saturating contact rate under a generalist predator is proposed. For a generalist predator which feeds on many types of prey, we assume that the predator can discriminate among susceptible and infected with each strain prey. First, mathematical analysis of the model with regard to invariance of nonnegativity, boundedness of solutions, nature of equilibria, persistence and global stability are analyzed. Second, the two strains will competitively exclude each other in the absence of predation with the strain with the larger reproduction number persisting. If predation is discriminate, then depending on the predation level, a dominant strain may occur. Thus, for some predation levels, the strain one may persist while for other predation levels strain two may persist. Furthermore, coexistence line and coexistent asymptotic-periodic solution are obtained when coexistence occur while heteroclinic is obtained when the two strains competitively exclude each other. Finally, the impact of predation is mentioned along with numerical results to provide some support to the analytical findings.

Stable coexistence in a Lotka-Volterra model with heterogeneous resources and intraguild predation

In this study we model population dynamics in a three-species food web with heterogeneous resources and intraguild predation by using a nonspatial Lotka-Volterra system with a density-dependent interaction of resource items. The model consists of two predators with an intraguild predation (IGP) relation competing for a common resource. The resource is subdivided into subpopulations of different quality that are distinguished by grazing rates of the two predators, contact rates between subpopulations and mortality rates. The proposed system describes an exchange of traits between species from distinct subpopulations by using a species interaction term. In particular, we examine the percentage of stable coexistence solutions versus resource carrying capacity and contact rates between distinct resource pools. We also present a numerical comparison of the percentage of stable food webs found for different numbers of subpopulations. While at high enrichment no stable coexistence was found in the IGP system with a single resource, our model predicts a stable coexistence of two IGP-related predators and resources at high and intermediate enrichment already at a low contact rate between subpopulations.

Coexistence phenomena and global bifurcation structure in a chemostat-like model with species-dependent diffusion rates

We study the competition of two species for a single resource in a chemostat. In the simplest space-homogeneous situation, it is known that only one species survives, namely the best competitor. In order to exhibit coexistence phenomena, where the two competitors are able to survive, we consider a space dependent situation: we assume that the two species and the resource follow a diffusion process in space, on top of the competition process. Besides, and in order to consider the most general case, we assume each population is associated with a distinct diffusion constant. This is a key difficulty in our analysis: the specific (and classical) case where all diffusion constants are equal, leads to a particular conservation law, which in turn allows to eliminate the resource in the equations, a fact that considerably simplifies the analysis and the qualitative phenomena. Using the global bifurcation theory, we prove that the underlying 2-species, stationary, diffusive, chemostat-like model, does possess coexistence solutions, where both species survive. On top of that, we identify the domain, in the space of the relevant bifurcation parameters, for which the system does have coexistence solutions.

Coexistence solutions of a periodic competition model with nonlinear diffusion

This paper is concerned with a spatially heterogeneous Lotka–Volterra competition model with nonlinear diffusion and nonlocal terms, under the Dirichlet boundary condition. Based on the theory of Leray–Schauder’s degree, we give sufficient conditions to assure the existence of coexistence periodic solutions, which extends some results of G. Fragnelli et al.

Coexistence and Numerical Solutions of the Unstirred Chemostat Model

This paper studies a competition model between two species for two resources in the chemostat with the Beddington-DeAngelis functional response. The sufficient condition to the coexistence of positive steady state solutions is obtained by the mathematical methods of the fixed point degree theory in cones. Finally, Some results of numerical simulations is presented to prove and complement the previous mathematical results by numerical computation method. Furthermore, the research result implies that two species in the biological environment can be coexistence after a long time.

전송 스케줄 및 사용자 위치 정보를 이용한 무선 인지 네트워크의 동일 주파수 대역 공존 방안

In cognitive radio networks, a secondary user opportunistically accesses an empty channel based on periodic sensing results for avoiding possible interference to the primary users. However, local sensing does not guarantee the full protection of the primary users because hidden primary receivers may exist within the interference range of the secondary transmitter. To protect primary systems and simultaneously to maximize utilization of the secondary users, we need to derive carefully designed coexistence solutions for various network scenarios. In this paper, we propose coexistence conditions without any harmful interference in accordance with the uplink/downlink schedule and user position. We have classified the coexistence conditions into four different scenario cases depending on the provided information to the secondary network basestations. Computer simulation results demonstrated that the proposed method can be applied to the real cognitive radio system to improve the communication probability of CR devices.

A Complete Design of Coexistence Information Service for Autonomous Decision-Making Systems in TV White Space

In this paper, we present a coexistence protocol design for a coexistence information service to provide coexistence solutions among dissimilar or independently operated autonomous decision-making networks in a wireless communication environment over, specifically but not limited to, TV white space (TVWS) frequency bands. The designed coexistence protocol for the coexistence information service has three main functionalities: (1) To collect basic information of subscribed TVWS networks; (2) To support generating neighbor lists for the TVWS networks based on the geography information and/or propagation parameters; (3) To provide necessary information for TVWS networks to make coexistence decisions. Both theoretical analysis and simulation results show that the designed coexistence information service ensures harmonious communications among dissimilar networks and is able to achieve coexistence over an area with the limited number of available channels in white space.

Orbital-selective crossover and Mott transitions in an asymmetric Hubbard model of cold atoms in optical lattices

We study the asymmetric Hubbard model at half filling as a generic model to describe the physics of two species of repulsively interacting fermionic cold atoms in optical lattices. We use dynamical mean-field theory to obtain the paramagnetic phase diagram of the model as a function of temperature, interaction strength, and hopping asymmetry. A Mott transition with a region of two coexistent solutions is found for all nonzero values of the hopping asymmetry. At low temperatures the metallic phase is a heavy Fermi liquid, qualitatively analogous to the Fermi-liquid state of the symmetric Hubbard model. Above a coherence temperature, an orbital-selective crossover takes place, wherein one fermionic species effectively localizes, and the resulting bad metallic state resembles the non-Fermi-liquid state of the Falicov-Kimball model. We compute observables relevant to cold atom systems such as the double occupation, the specific heat, and entropy, and characterize their behavior in the different phases.

Rotational Listening Strategy for IEEE 802.15.4 Wireless Body Networks

In recent years, interests in the application of wireless body network (WBN) have grown considerably. Wireless body sensor nodes assume deploying a stationary sensor network over a human body area. Among the well-known specifications, IEEE 802.15.4 originally designed for low-power, low-rate, and short-distance wireless personal area networks (WPANs) has become one of the promising candidates for interconnections between wireless sensor nodes. IEEE 802.15.4 uses a modified carrier-sense multiple access with collision avoidance (CSMA/CA) MAC protocol to access channel for transmission data; however, it suffers from inefficient channel utilization because the physical carrier sensing is only performed after the backoff period. In this paper, a rotational listening strategy (RLS) is proposed to increase the rate of successful transmission for WBN. The channel access period is logically partitioned into a number of mini-slots that are individually allocated to nodes. In this case, inefficient channel utilization and collisions can be resolved simultaneously, meanwhile retaining fairness criterion. In addition, an enhanced RLS is proposed to handle the load unbalance situation among nodes. This paper also provides a coexistence solution for the situation where there are nodes without RLS associating with an RLS-enabled WSN. Analytical and numerical simulations are both studied to evaluate the performance of RLS. Both results illustrate that RLS indeed improves transmission efficiency as well as energy consumption.

On nonlocal parabolic steady-state equations of cooperative or competing systems

Some systems of parabolic equations with nonlocal initial conditions are studied. The systems arise when considering steady-state solutions to diffusive age-structured cooperative or competing species. Local and global bifurcation techniques are employed to derive a detailed description of the structure of positive coexistence solutions.

Exact multiplicity of coexistence solutions to the unstirred chemo-stat model with the plasmid and internal inhibitor

Exact multiplicity of coexistence solutions to the unstirred chemo-stat model with the plasmid and internal inhibitor

Effect of competition on niche dynamics of syntopic grazing ungulates: contrasting the predictions of habitat selection models using stable isotope analysis

Background: Theories of density-dependent habitat selection provide two solutions for co-existence of competing species. The niche compression hypothesis predicts that species reduce their respective niche breadths in response to inter-specific competition. Alternatively, if the species have similar resource preferences, the subordinate species may be forced to expand its niche to incorporate secondary resources. Aim: Determine whether grazing ungulate species partition the resource by compression or expansion of dietary niches. Organisms: Black wildebeest (Connochaetes gnou) and blue wildebeest (C. taurinus). Methods: Stable carbon and nitrogen isotope analysis of faeces. Isotopic niche breadths are compared across allopatric and sympatric wildebeest populations in South African grasslands. Results: Stable carbon and nitrogen isotope niche breadths of the two wildebeest species were virtually identical. In sympatry, however, black wildebeest had a narrower δ13C niche breadth (indicating almost exclusive use of C4 grass), whereas blue wildebeest had a wider δ13C niche breadth (indicating significant contributions from C3 sources). Blue wildebeest also had a wider δ15N niche breadth than sympatric black wildebeest. Moreover, the δ13C niche breadths of sympatric black wildebeest and blue wildebeest were narrower and wider, respectively, than those of allopatric populations of either species. Conclusions: Isotope niche dynamics across allopatric and sympatric populations arise due to the combined effects of competition and habitat heterogeneity on resource use. Although results for black wildebeest resemble niche compression, this hypothesis cannot explain patterns observed in blue wildebeest. Expansion of the blue wildebeest niche, and restricted niche breadth of black wildebeest, is consistent with predictions of a shared preference model in which black wildebeest are the dominant competitor. When competition is operating, differences in the way species use secondary resources can have an important role in structuring grazer assemblages.