جستجوی مقالات مرتبط با کلیدواژه "انشعاب" در نشریات گروه "ریاضی"

‎In this article‎, ‎we present an $SIR$ model with a general nonlinear incidence rate‎, ‎assuming a $100\%$ effective vaccine‎. ‎This system has a disease-free equilibrium point‎, ‎corresponding to which a basic reproduction number $\mathscr{R}_0$‎​ ‎is obtained‎. ‎For $\mathscr{R}_0 > 1$‎, ‎the system will also have an endemic equilibrium point‎. ‎We study the local and global stability of these equilibrium points‎. ‎Considering the change in the stability status of the equilibrium points with the change of one of the parameters‎, ‎we will examine the existence of a transcritical bifurcation‎. ‎Additionally‎, ‎we calculate the sensitivity index of $\mathscr{R}_0$​‎, ‎which essentially determines the susceptibility of the system to the existing parameters‎. ‎Finally‎, ‎we examine the obtained results with numerical examples‎.

  In population dynamics, discrete-time dynamical systems have been used to describe interaction between ecological species. Comparing to continuous-time dynamical systems, discrete-time models are more suitable to describe populations with non overlapping generations. These models in general produce rich and complex dynamical behaviors.Among various population interaction, predator-prey models play a fundamental rule in mathematical ecology. The dynamics of predator-prey system is greatly depend on the implementation of the functional response, the availability of prey for predation. In this paper we consider a planar system which describes a predator-prey model. In order to reveal comprehensive dynamics of the system, we employee theoretical tools such as center manifold theorem along with numerical tools based on numerical continuation method.

Our analysis is based on theoretical and numerical techniques. We first determine all fixed points of the system and conditions under which these points may undergo different bifurcations. To reveal more dynamics of the system, we also use numerical bifurcation methods and numerical simulations, which further examine the obtained analytical results.

For the resented discrete-time predator-prey system, we compute several bifurcation curves, all possible codimension-1 and codimension-2 bifurcations on thses curves along with their corresponding normal form coefficients. By branch switching technique and employing software package MatcontM, we compute stability boundaries for several cycles up to period 32. We also use numerical simulation, to compute basin of attraction and strange attractor emerging around a Neimark-Sacker bifurcation.

We can highlight the following results from this paper. Detection and location of all fixed points of a discrete-time predator pray system. Computing all possible codimension-1 and -2 bifurcation and their corresponding normal form coefficients which in turn reveal criticality of the bifurcation points and determine if extra bifurcation curves can emanate from each detected bifurcation. Computing orbits up to period 32 which determine stability thresholds for different cycles. Computing basin of attraction and strange of attractor which emerge around a Neimark-Sacker bifurcation by means of numerical simulation technique.