Vol. 6, No. 3 (2017): Regular Issue

Implementation of any policy involves negotiation between multiple actors, and is therefore susceptible to a dynamic systems modelling approach. In this paper, we make an attempt to develop a family of dynamic systems models of policy implementation in such a multi-actor world by translating an existing, semi-quantitative, application of two theoretical approaches, Contextual Interaction Theory (CIT) and Participatory Action Research (PAR), into a quantitative dynamic framework. We explore various alternative actor-based dynamic systems for this proposed Participatory Contextual Interaction Theory (PCIT), including linear, piecewise linear, and strongly nonlinear models. Analytical results are supplemented with results of numerical simulations. One of the goals of the modelling exercise is to advance the actor dynamics module in the APoLUS land use cellular automata model; illustrative examples of the incorporation of actor dynamics models developed in the present paper into the computation of APoLUS transition potentials are provided.

A set stabilizing gain generator (SSGG) framework is developed along with dynamic controllers and observers to regulate and estimate the state trajectories of an arbitrary set of three or more open loop unstable linear time invariant dynamic system models of variable dimensions in the state space form. The individual systems in the set are assumed to be controllable and observable. An algorithm is suggested for Single Input (SI) simultaneous stabilization and Single Output (SO) simultaneous observation. This is then extended to a set of Multiple Input (MI) and Multiple Output (MO) models. A dynamic observer based dynamic controller is also formulated for SISO and MIMO systems. The algorithm is then extended to accommodate simultaneous stabilization and observation of system models of variable dimensions. It is finally shown that the dynamic controllers and observers guarantee a certain stability radius against bounded time-varying uncertainty for the entire set which their static counterparts fail to assign. Suitable SI, SO, SISO and MI, MO, MIMO examples are provided.

In this paper, a Freidlin-Wentzell type large deviation principle is established for the stochastic integrodifferential equation driven by finite dimensional Brownian motion. Both the additive and multiplicative noise cases are considered here. Large deviation principle for additive noise case is established via contraction principle whilst weak convergence approach is employed to obtain the same for the multiplicative noise case.

In this work, we investigate three completely integrable model equations used to describe shallow water waves. A variety of techniques will be sued to determine abundant solutions, of distinct physical structures, for each model. The three models give soliton solutions, periodic solutions, rational hyperbolic functions and rational solutions as well.

This paper deals with the two species chemotaxis system in a bounded domain R3 under different boundary conditions. Explicit lower bounds for blow up time are obtained by using differential inequality technique under suitable assumptions on the data.

Complex dynamics of small particles under the action of acoustic radiation force is considered. This work extends the previous studies of Ostrovsky & Sarvazyan (2009) and Ostrovsky (2015) in two aspects. Firstly, here the particle material can have an arbitrary compressibility and sound speed. Secondly, in addition to the viscosity effect described by the Stokes drag force, the Boussinesq–Basset drag force and the inertial force which includes added mass effect are accounted for. Although, as was assumed in the earlier publications, the latter effects are usually small, nevertheless their influence can be noticeable in specific cases considered in this paper. The control of particle motion by switching of acoustic modes is also studied for particles of different properties. Quantitative estimates are given for particles made of different materials.

In this paper, period-m motions on the bifurcation trees of peiod-1 to chaos for nonlinear cable galloping are studied analytically, and the analytical solutions of the period-m motions in the form of the finite Fourier series are obtained through the generalized harmonic balance method, and the corresponding stability and bifurcation analyses of the period-m motions in the galloping system of nonlinear cable are carried out. The bifurcation trees of period-m motions to chaos are presented through harmonic frequency-amplitudes. Numerical illustrations of trajectories and amplitude spectra are given for periodic motions in nonlinear cables. From such analytical solutions of periodic motions to chaos, galloping phenomenon in flow-induced vibration can be further understood.

This paper is concerned with a diffusive Leslie-Gower predator-prey system with ratio dependent Holling type III functional response subject to Neumann boundary conditions. By linearizing the system at the positive constant steady-state solution and analyzing the associated characteristic equation in detail, local stability, existence of a Hopf bifurcation at the coexistence of the equilibrium and stability of bifurcating periodic solutions of the system in the absence of diffusion are studied. Furthermore, Turing instability and Hopf bifurcation analysis for the system with diffusion are studied. Finally, numerical simulations are provided in order to verify our theoretical results.

In this paper we study the controllability of linear and nonlinear stochastic fractional systems driven by Lévy noise. Here we use the Lévy-Itô decomposition of an arbitrary Lévy process into Brownian and Poisson parts. The necessary and sufficient conditions for controllability of the linear system is obtained. Also, the nonlinear system is shown controllable under the assumption that the corresponding linear system is controllable and using the Banach contraction principle.