We use a differential constitutive equation to model the flow of a viscoelastic flow in a cross-slot geometry, which is known to exhibit bistability above a critical flow rate. The novelty lies in two asymmetric modifications to the geometry, which causes a change in the bifurcation diagram such that one of the stable solutions becomes disconnected from the solution at low flow speeds. First we...

This paper investigates dynamics of double pendulum subjected to vertical parametric kinematic excitation. It includes detailed bifurcation diagrams in two parameters space (excitation's frequency and amplitude) for both oscillations and rotations in the domain of periodic solutions.

We study the saddle-node bifurcation of a spatially homogeneous oscillation in a reactiondiffusion system posed on the real line. Beyond the stability of the primary homogeneous oscillations created in the bifurcation, we investigate existence and stability of wave trains with large wavelength that accompany the homogeneous oscillation. We find two different scenarios of possible bifurcation di...

We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams.

Gray, Scott and their collaborators proposed the model analyzed in our paper in the 80’s. The model describes an autocatalytic mechanism in isothermal systems where the reaction rate is increased by strengthening the concentration of one of the products. The chemical reaction (Fig. 1) occurs in a continuously stirred tank reactor (CSTR) and it involves two reactants X and Y with concentrations ...

This study estimates a parameter space from only two time-series data sets in order to predict when critical transition occurs caused by saddle-node bifurcation. By estimating the space, we can plot bifurcation diagram corresponding original diagram. In addition, Lyapunov exponent also be approximated estimated and corresponds Thereby, expect that value at which is predicted. numerical experime...

This paper is concerned with the nonlinear multiparameter elliptic eigenvalue problem u′′(r) + N − 1 r u′(r) + μu(r)− k ∑ i=1 λifi(u(r)) = 0, 0 < r < 1, u(r) > 0, 0 ≤ r < 1, u′(0) = 0, u(1) = 0, where N ≥ 1, k ∈ N and μ, λi ≥ 0 (1 ≤ i ≤ k) are parameters. The aim of this paper is to study the asymptotic properties of eigencurve μ(λ, α) = μ(λ1, λ2, · · · , λk, α) with emphasis on the phenomenon ...

Bifurcations of periodic, quasi-periodic and chaotic oscillations are most frequently observed in forced nonlinear circuits containing saturable inductors, whose dynamics are described by nonautonomous di erential equations with periodic external forcing terms. A Poincar e mapping is commonly applied to the study of the bifurcation phenomena. We present some elementary discussion of the codimen...

We prove compactness properties along the branches of semi-stable and unstable solutions –whose Morse index is at most one– of the Dirichlet boundary value problem −∆u = λf(x) (1−u)2 on a bounded domain Ω ⊂ R , provided 1 ≤ N ≤ 7. As a byproduct, we are able to follow the second branch of the bifurcation diagram and prove the existence of a second solution for λ in a natural range. We also show...

In the paper, some basic dynamic properties of a new fractional-order hyperchaotic system were firstly investigated, such as the phase trajectory, bifurcation diagram, Lyapunov exponent etc. Then the paper designed an analog circuit to implement the fractional-order hyperchaotic system. The results from the circuit were consistent with those from the numerical analysis, and thus the hyperchaoti...