Vol. 5, No. 3 (2016): Regular Issue

We continue our study of the dynamics of the yeast cell division cycle, in particular a feedback model where cells in one fixed part of the cycle, the Signaling region, affect the growth of cells in another part of the cycle, the Responsive region. This causes cells to cluster together as they pass through their cell division cycles, a known biological phenomenon that had been previously unexplained. In previous work, these regions were assumed to have disjoint interiors. We consider the dynamics when oscillators are coupled directly to themselves by allowing the responsive and signaling regions to overlap. We see that although the dynamics in an important subspace are largely preserved, the dynamics of the system in the full phase space exhibit less clearly quantifiable behavior. While in previously studied models, stability in the clustered subspace implies stability in the full phase space, here this is not the case, and the clustered subspace only unreliably predicts the behavior in the full phase space.

This paper discusses bifurcations in nonlinear vibroimpact system. It is a discontinuous dynamical system. We were studying stability and bifurcations in specific two-body two-degree-of-freedom vibroimpact system by numerical parameter continuation method. We adapted parameter continuation technique for this system. Theoretical basis for dynamic characteristics composition was presented in [1]. The instability zones and bifurcation points for loading curves were determined in [1] under excitation amplitude variation. In this paper we investigate the instability zones and bifurcation points under variation of excitation frequency when we consider the frequency-amplitude response. We have observed phenomena unique for nonsmooth systems with discontinuous right-hand side: discontinuous bifurcation points where set-valued Floquet multipliers cross the unit circle by jump. At these points monodromy matrix is changed by jump too. We also have observed chattering regimes leading to chaos.

In this paper we consider a ratio dependent Holling Tanner predator prey model with type II functional responses. We analyzed the local stability, phase portraits, existence and uniqueness of stable limit cycles and Hopf bifurcation. The ranges of the parameter involved are provided under which the unique interior equilibrium can be determined for a stable (or an unstable) node or focus without diffusion. Furthermore the Turing instability analysis of the system with diffusion are studied. Numerical simulations using MATLAB are carried out to demonstrate the theoretical results obtained.

The objective of this work is to review and elaborate an approximation method of the transfer functions of both semi-infinite and finite homogeneous plane thermal diffusive interfaces, in view to use in robust control applications and to obtain accurate time responses. Novel models are proposed based on the fractional order integration found naturally when modelling diffusive interfaces. The models are verified by checking with the existing exact responses. The results obtained in this part of the work show a very good approximation of the transfer functions of the systems when using a rational representation in both frequency and time domains for several inputs such as the impulse and the step.

In this paper we propose a new approach that allows a mobile robot to follow a chaotic trajectory, which is a projection of the strange attractor of any deterministic chaotic system, on the xoy plane. This approach is reminiscent of the master-slave synchronization. The desired chaotic curve is expressed in terms of a virtual reference robot. The suboptimal State Dependent Riccati Equation (SDRE) control is applied to achieve synchronization between the real and virtual robots. We demonstrate two examples of this approach, leading the robot system to a synchronization with Rossler and Lorenz strange attractor’s xoy projections.

This paper investigates the dynamics of two coupled Mathieu equations. The coupling functions involve both delayed and nondelayed terms. We use a perturbation method to obtain a slow flow which is then studied using Routh-Hurwitz stability criterion. Analytic results are shown to compare favorably with numerical integration. The numerical integrator, DDE23, is shown to inadvertently add damping. It is found that the nondelayed coupling parameter plays a significant role in the system dynamics. We note that our interest in this problem comes from an application to the design of nuclear accelerators.

Dynamic wake models have been evolved from the earliest, threedegree- of-freedom models (derived from momentum theory) to full finite-state models derived from potential flow theory by a formal Galerkin method. These models are widely used in industry, but still have some drawbacks that need to be remedied. These drawbacks include: 1.) lack of good convergence both on the disk and off the disk (one can use one or the other but not both), 2.) poor results downstream in the limit of shallow skew angles, 3.) poor convergence inside of the rotor wake, 4.) lack of the effect of wake contraction. In this paper, a blended model adopted applications of adjoint theorem, a special change of variables to overcome these obstacles. The resultant model is well behaved in all regimes and is applicable to use in realistic problems of flight simulation.