the modeling investigation in this paper discusses the system level effects of a toxicant on a three species food chain system. in the models, we have assumed that the presence of top predator reduces the predatory ability of the intermediate predator. the stability analysis of the models is carried out and the sufficient conditions for the existence and extinction of the populations under the ...

We study the bifurcation loci of quadratic (and unicritical) polynomials and exponential maps. We outline a proof that the exponential bifurcation locus is connected; this is an analog to Douady and Hubbard’s celebrated theorem that (the boundary of) the Mandelbrot set is connected. For these parameter spaces, a fundamental conjecture is that hyperbolic dynamics is dense. For quadratic polynomi...

For a family of continuous-time dynamical systems with two angle variables, a resonance is a set of parameter values such that some integer combination of the (lifted) angles remains bounded for some orbits. For weak coupling of an unfolding of a saddle-node periodic orbit with an oscillator, it is shown that the low order resonances have at least a certain amount of bifurcation structure. Furt...

The positive solutions of a Laplace equation with a superlinear nonlinear boundary condition on a bounded domain are studied. For higher-dimensional domains, it is shown that non-constant positive solutions bifurcate from a branch of trivial solutions at a sequence of bifurcation points, and under additional conditions on nonlinearity, the existence of a non-constant positive solution for any s...

We study a Holling II predator-prey model with frequency-dependent fitness and nonzero constant harvesting rate of prey. It is shown that the model has at most one hyperbolic positive equilibrium which may be a node, focus or a center and can exhibit the Hopf bifurcation or Heteroclinic bifurcation when parameters vary in a small neighborhood of the values of parameters. Meanwhile, a sufficient...

Paper constructs approximate analytical expressions of periodic disequilibrium fluctuations business cycles occurring in connection with Hopf bifurcations in nonlinear problems of economic interactions described by four-dimensional continuous time dynamical systems. Two nonlinear macrodynamic models are employed as tests models. The region of equilibrium stability in parameter space is obtained...

Percutaneous coronary intervention in the setting of coronary bifurcation lesions is associated with increased risk for complications. The goal of this manuscript is to review the currently available classifications for coronary artery bifurcation lesions with a guide to the use of specific coronary bifurcation techniques based on lesion characteristics

In the analysis of stability in bifurcation problems it is often assumed that the (appropriate reduced) equations are in normal form. In the presence of symmetry, the truncated normal form is an equivariant polynomial map. Therefore, the determination of invariants and equivariants of the group of symmetries of the problem is an important step. In general, these are hard problems of invariant t...

We introduce a method for tracking nonlinear oscillations and their bifurcations in nonlinear dynamical systems. Our method does not require a mathematical model of the dynamical system nor the ability to set its initial conditions. Instead it relies on feedback stabilizability, which makes the approach applicable in an experiment. This is demonstrated with a proofof-concept computer experiment...

Abstract In this paper, a kind of magnetorheological elastomer sandwich plate is proposed. The novel nonlinear differential term applied to describe the force-displacement curve elastomer. constitutive model system established using Hamilton Modeling Principle. By Galerkin dispersion, response equation obtained, and its stochastic dynamic behavior discussed. numerical results are simulated by M...