In this paper, we develop a criterion to calculate the multiplicity of a multiple focus for general predator prey systems. As applications of this criterion, we calculate the most multiplicity of a multiple focus in a predator prey system with nonmonotonic functional response p(x) = x ax+bx+1 studied by Zhu, Campbell and Wolkowicz [26] and prove that the degenerate Hopf bifurcation is of codime...

We analyse the dynamical behaviour of a simple, widely used model that integrates epidemiological dynamics with disease control and economic constraint on the control resources. We consider both the deterministic model and its stochastic counterpart. Despite its simplicity, the model exhibits mathematically rich dynamics, including multiple stable fixed points and stable limit cycles arising fr...

In certain regions of the moduli space of K3 and Calabi-Yau manifolds, D-branes wrapped on non-supersymmetric cycles may give rise to stable configurations. We show that in the orbifold limit, some of these stable configurations can be described by solvable boundary conformal field theories. The world-volume theory of N coincident branes of this type is described by a non-supersymmetric U(N) ga...

The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are...

Networks of neurons produce diverse patterns of oscillations, arising from the network's global properties, the propensity of individual neurons to oscillate, or a mixture of the two. Here we describe noisy limit cycles and quasi-cycles, two related mechanisms underlying emergent oscillations in neuronal networks whose individual components, stochastic spiking neurons, do not themselves oscilla...

Stable isotopes of carbon and nitrogen are increasingly used in marine ecosystems, for ecological and environmental studies. Here, we examine some applications of stable isotopes as ecological integrators or tracers in seagrass ecosystem studies. We focus on both the use of natural isotope abundance as food web integrators or environmental tracers and on the use of stable isotopes as experiment...

We call a boolean formula (in CNF) stable acyclic if the associated digraph is free of a certain type of cycles. We show that satisfiability and recognition are polynomial–time solvable problems for stable acyclic formulas. Further, we show that a minimal unsatisfiable formula is stable acyclic if and only if the number of clauses exceeds the number of variables exactly by one (this subclass of...

conclusions in lighting conditions, most of t-res was isomerized to the other isomer cis-resveratrol. t-res is unstable in alkali ph and when exposed to light. t-res was quite stable at other conditions, and several freeze-thaw cycles did not have any effect on its stability. results our findings revealed that t-res was quite stable in different temperatures ranging from -70 °c to 25 °c, and ac...

the focus of studies in the field of passive walking has often been on straight walking, while less attention has been paid to the field of turning motions. in this paper, the passive motions of a finite width rimless wheel as the simplest 3d model of passive biped walkers was investigated with a focus on turning motions. for this purpose, the hybrid model of the system consisting of continuous...