A structured model of bioreactor for an activated sludge process was presented. The stability and bifurcation characteristics of the model are investigated, the bifurcation analysis of the model shows static and complex dynamic behavior (periodic and complex) over a wide range of the model parameters. The model exhibits a new interesting behavior (in some range of parameters) including four sta...

Oneand two-parameter Hopf bifurcation behavior is analyzed for several variants of the Citri-Epstein mechanism of the chlorite-iodide reaction. The coefficients of an equation for the amplitude of oscillations (the universal unfolding of the Hopf bifurcation) are evaluated numerically. Local bifurcation diagrams and bifurcation sets are derived from the amplitude equation. Suband supercritical ...

Asymptotic behavior of a recurrent neural network changes qualitatively at certain points in the parameter space, which are known as \bifurcation points". At bifurcation points, the output of a network can change discontinuously with the change of parameters and therefore convergence of gradient descent algorithms is not guaranteed. Furthermore, learning equations used for error gradient estima...

In this paper the dynamics of a discrete-time prey-predator system is investigated in the closed first quadrant . The existence and stability of fixed points are analyzed algebraically .The conditions of existence for flip bifurcation is derived by busing center manifold theorem and bifurcation theory. Numerical simulations not only illustrate our results but also exhibit complex dynamical beha...

In two-parameter systems with symmetry two steady state bifurcation points of diierent symmetry types coalesce generically within one point. Under certain group theoretic conditions involving the action of the symmetry group on the kernels, we show that secondary Hopf bifurcation is borne by the mode interaction. We explain this phenomenon by using linear representation theory. For motivation a...

In this note, we present a simple one-parameter family of interval maps which has a direct bifurcation from order to chaos and then another direct bifurcation from chaos back to order. (See also [4, 5].) In fact, for this family of interval maps, the creation of the first non-fixed periodic point is more complicated than we expect. It is the limit point of a series of bifurcations of period 2n ...

For a two-neuron network with self-connection and time delays, we carry out stability and bifurcation analysis. We establish that a Hopf bifurcation occurs when the total delay passes a sequence of critical values. The stability and direction of the local Hopf bifurcation are determined using the normal form method and center manifold theorem. To show that periodic solutions exist away from the...