<p style='text-indent:20px;'>We study integrability and bifurcations of a three-dimensional circuit differential system. The emerging periodic solutions under Hopf bifurcation zero-Hopf is investigated using the center manifolds averaging theory. equilibrium non-isolated lies on line filled in with equilibria. A Lyapunov function found global stability origin proven case when it simple lo...

Among the most important topological constructions are Hopf fibrations. That they both play an important role in topology itself and have numerous physical applications lends credence to this statement. In this paper, I will discuss some of these applications as motivation for mathematicians to learn about the physical significance of the Hopf fibration in greater detail than that presented her...

with A a diagonal matrix. Appropriate boundary and initial conditions are given. The amplification matrix Q(£) need not be diagonal. However, he required that |Q(£)| ^ 1We use certain results in matrix theory and Wiener-Hopf factorization to replace this restrictive assumption by certain reasonable assumptions on accuracy of Q(£) and smoothness of an associated positive-definite symmetric matri...

We study a delay diierential equation modelling the harmonic oscillator with forcing which depends on the state and the derivative of the state at some time in the past. We perform a linearized stability analysis of the equation and describe the location of Hopf and steady state bifurcations in the parameter space. A complete description of the location of points in parameter space where the ch...

In this paper, an optimal Wiener-Hopf decoupling controller formula is obtained which is expressed in terms of rational matrices, thereby readily allowing the use of state-space algorithms. To this end, the characterization formula for the class of all realizable decoupling controller is formulated in terms of rational functions. The class of all stabilizing and decoupling controllers is parame...

Hopf bifurcations from time periodic rotating waves to two frequency tori have been studied for a number of years by a variety of authors including Rand and Renardy. Rotating waves are solutions to partial differential equations where time evolution is the same as spatial rotation. Thus rotating waves can exist mathematically only in problems that have at least SO(2) symmetry. In this paper we ...

We formulate and investigate a relatively new modeling paradigm by which spatially segregated dynamically active units communicate with each other through a signaling molecule that diffuses in the bulk medium between active units. The modeling studies start with a simplified setting in a onedimensional space, where two dynamically active compartments are located at boundaries of the domain and ...

We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on SUq(2) . The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector...

We construct static and time dependent exact soliton solutions for a theory of scalar fields taking values on a wide class of two dimensional target spaces, and defined on the four dimensional space-time S 3 × IR. The construction is based on an ansatz built out of special coordinates on S 3. For the case where the target space is the sphere S 2 , the infinite set of solutions have non-trivial ...