Many applications require fast data transfer over high speed and long distance networks. Compound TCP(CTCP) is a novel congestion control algorithm for high-speed and long delay networks. This paper develops a discrete time dynamic feedback model of a congestion control system with CTCP under random early detection (RED). We find that periodic doubling bifurcation occurs when varying the RED co...

We consider infinite Prandtl number convection with rotation which is the basic model in geophysical fluid dynamics. For the rotation free case, the rigorous analysis has been provided by Park [15, 16, 17] under various boundary conditions. By thoroughly investigating We prove in this paper that the solutions bifurcate from the trivial solution u = 0 to an attractor ΣR which consists of only on...

A theory is provided to analyze the dynamics of delay-coupled pools of spiking neurons based on stability analysis of stationary firing. Transitions between stable and unstable regimes can be predicted by bifurcation analysis of the underlying integral dynamics. Close to the bifurcation point the network exhibits slowly changing activities and allows for slow collective phenomena like continuou...

A predator-prey model in presence of alternative prey is proposed. Existence and local stability conditions for interior equilibrium points are derived. Global stability conditions for interior equilibrium points are also found. Bifurcation analysis is done with respect to predator's searching rate and handling time. Bifurcation analysis confirms the existence of global stability in presence of...

A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal dimension of the chaotic set for such a bifurcation. Our analysis and numerical computations in both two- and three-degrees-of-freedom systems suggest a strik...

We consider parameter-dependent, continuous-time dynamical systems under discretizations. It is shown that fold-Hopf singularities are O(h)-shifted and turned into fold-Neimark-Sacker points by one-step methods of order p. Then we analyze the effect of discretizations methods on the local bifurcation diagram near BogdanovTakens and fold-Hopf singularities. In particular we prove that the discre...

Extended abstract We show that the cusp catastrophe model explains the crash of stock exchanges much better than alternative linear and logistic models. On the data of U.S. stock markets we demonstrate that the crash of October 19, 1987 may be better explained by cusp catastrophe theory, which is not true for the crash of Sept. 11, 2001. With the help of sentiment measures, such as index put/ca...

An epidemiological model is presented that provides a comprehensive description of the transmission pathways involved for recurrent tuberculosis (TB), whereby cured individuals can become reinfected. Our main goal is to determine conditions that lead to the appearance of a backward bifurcation. This occurs when an asymptotically stable infection free equilibrium concurrently exists with a stabl...

Theoretical demographic models with an accompanying experimental program provide an important framework to study the life history of organisms. In this paper we seek to understand the fitness characteristics of gregarine parasites and how they are shaped by their own life cycle stages inside and outside an insect host. The population model is a continuous time dynamics for the parasite stages, ...

Abstract. Many applications give rise to separable parameterized equations, which have the form A(y, μ)z + b(y, μ) = 0, where z ∈ R , y ∈ R, μ ∈ R, and the (N + n)×N matrix A(y, μ) and (N + n) vector b(y, μ) are C-Lipschitzian in (y, μ) ∈ Ω ⊂ R × R. We present a technique which reduces the original equation to the form f(y, μ) = 0, where f : Ω → R is C-Lipschitzian in (y, μ). This reduces the d...