The set of steady state solutions to a reaction–diffusion equation modeling an autocatalytic chemical reaction is completely determined, when the reactor has spherical geometry, and the spatial dimension is n= 1 or 2 for any reaction order, or n 3 for subcritical reaction order. Bifurcation approach and analysis of linearized problems are used to establish exact multiplicity and precise global ...

The bifurcation diagram of a truncation to six degrees of freedom of the equations for quasi-geostrophic, baroclinic ow is investigated. Period doubling cascades and Shil'nikov bifurcations lead to chaos in this model. The low dimension of the chaotic attractor suggests the possibility to reduce the model to three degrees of freedom. In a physically comprehensible limit of the parameters this r...

The bifurcation diagram of a truncation to six degrees of freedom of the equations for quasi-geostrophic, baroclinic flow is investigated. Period doubling cascades and Shil’nikov bifurcations lead to chaos in this model. The low dimension of the chaotic attractor suggests the possibility to reduce the model to three degrees of freedom. In a physically comprehensible limit of the parameters this...

The biharmonic supercritical equation ∆u = |u|p−1u, where n > 4 and p > (n + 4)/(n − 4), is studied in the whole space R as well as in a modified form with λ(1 + u) as right-hand-side with an additional eigenvalue parameter λ > 0 in the unit ball, in the latter case together with Dirichlet boundary conditions. As for entire regular radial solutions we prove oscillatory behaviour around the expl...

In this article, we study parameter-dependent systems of reaction-diffusion equations on the sphere, which are equivariant under the group SO(3) of all rigid rotations on a sphere. Two main types of spatial-temporal patterns that can appear in such systems are rotating waves (equilibrium in a co-rotating frame) and modulated rotating waves (periodic solution in a corotating frame). The transiti...

It is used the Chua circuit to demonstrate the possibility of obtaining synchronization of chaos with numerical simulations of a coupled nonlinear system consisting of two coupled non-identical circuits. Synchronization is demonstrated through a correlation diagram while the dynamic behavior is explained with a bifurcation diagram. One of the circuit has an additional noise source, while to the...

In this paper, the dynamic characteristics of fractional Duffing system are analyzed and studied by using improved short memory principle method. This method has small amount calculation high precision, can effectively improve problem large caused order. The influence frequency change on performance is nonlinear analysis methods, such as Phase Portrait, Poincare Map Bifurcation Diagram. Moreove...

We present a rigorous mathematical analysis of a discrete dynamical system modeling plant pattern formation. In this model, based on the work of physicists Douady and Couder, fixed points are the spiral or helical lattices often occurring in plants. The frequent occurrence of the Fibonacci sequence in the number of visible spirals is explained by the stability of the fixed points in this system...