149 research outputs found
Equivariant Simplicial Cohomology With Local Coefficients and its Classification
We introduce equivariant twisted cohomology of a simplicial set equipped with
simplicial action of a discrete group and prove that for suitable twisting
function induced from a given equivariant local coefficients, the simplicial
version of Bredon-Illman cohomology with local coefficients is isomorphic to
equivariant twisted cohomology. The main aim of this paper is to prove a
classification theorem for equivariant simplicial cohomology with local
coefficients.Comment: 25 page
Revealing Hidden Genuine Tripartite Nonlocality
Nonlocal correlations arising from measurements on tripartite entangled
states can be classified into two groups, one genuinely way nonlocal and
other local with respect to some bipartition. Still, whether a genuinely
tripartite entangled quantum state can exhibit genuine way nonlocality,
remains a challenging problem so far as measurement context is concerned. Here
we introduce a novel approach in this regard. We consider three tripartite
quantum states none of which is genuinely way nonlocal in a specific Bell
scenario (three parties, two measurements per party, two outcomes per
measurement), but they can exhibit genuine way nonlocality when the initial
states are subjected to stochastic local operations and classical communication
(SLOCC). So, genuine way nonlocality is a resource, which can be revealed
by using a sequence of measurements.Comment: 10 pages, 2 figures, revtex, comments welcom
Impact of predator fear on two competing prey species
Predator-prey interaction is a fundamental feature in the ecological system. The majority of studies have addressed how competition and predation affect species coexistence. Recent field studies on vertebrate has shown that fear of predators can influence the behavioural pattern of prey populations and reduce their reproduction. A natural question arises whether species coexistence is still possible or not when predator induce fear on competing species. Based on the above observation, we propose a mathematical model of two competing prey-one predator system with the cost of fear that affect not only the reproduction rate of both the prey population but also the predation rate of predator. To make the model more realistic, we incorporate intraspecific competition within the predator population. Biological justification of the model is shown through positivity and boundedness of solutions. Existence andstability of different boundary equilibria are discussed. Condition for the existence of coexistence equilibrium point is derived from showing uniform persistence. Local as well as a global stability criterion is developed. Bifurcation analysis is performed by choosing the fear effect as the bifurcation parameter of the model system. The nature of the limit cycle emerging through a Hopf bifurcation is indicated. Numerical experiments are carried out to test the theoretical results obtained from this model
Dynamics of A Discrete-Time Ecogenetic Predator-Prey Model
This article considers a discrete-time model of two genetically distinguished predator population and one prey population. The existence and nature of the boundary and positive fixed points are examined. The sufficient criterion for Neimark-Sacker bifurcation (NSB) is derived. It is observed that the system behaves in a chaotic way when a specific set of system parameters is selected, which are controlled by a hybrid control method. Examples are presented to illustrate our conclusions
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