Search results for "dynamical system"
showing 10 items of 523 documents
Adsorption Active Diblock Copolymers as Universal Agents for Unusual Barrier-Free Transitions in Stimuli-Responsive Brushes
2021
We reconsider a recently proposed design for smart responsive brushes, which is based on a conformational transition in very dilutely embedded block copolymers with a surface active block (Qi et al., Macromolecules 53, 5326, 2020). Under certain conditions, the transition acquires an unusual character: it remains very sharp, but the barrier separating the adsorbed and desorbed states disappears completely. We show that these features are very robust with respect to changing almost all system parameters: the lengths of the inert and active blocks of the minority chain, the brush length, its density, and its polydispersity. The only relevant condition is that the inert block of the minority c…
Universality for the breakup of invariant tori in Hamiltonian flows
1998
In this article, we describe a new renormalization-group scheme for analyzing the breakup of invariant tori for Hamiltonian systems with two degrees of freedom. The transformation, which acts on Hamiltonians that are quadratic in the action variables, combines a rescaling of phase space and a partial elimination of irrelevant (non-resonant) frequencies. It is implemented numerically for the case applying to golden invariant tori. We find a nontrivial fixed point and compute the corresponding scaling and critical indices. If one compares flows to maps in the canonical way, our results are consistent with existing data on the breakup of golden invariant circles for area-preserving maps.
Drilling Systems: Stability and Hidden Oscillations
2013
There are many mathematical models of drilling systems Despite, huge efforts in constructing models that would allow for precise analysis, drilling systems, still experience breakdowns. Due to complexity of systems, engineers mostly use numerical analysis, which may lead to unreliable results. Nowadays, advances in computer engineering allow for simulations of complex dynamical systems in order to obtain information on the behavior of their trajectories. However, this simple approach based on construction of trajectories using numerical integration of differential equations describing dynamical systems turned out to be quite limited for investigation of stability and oscillations of these s…
Stochastic analysis of external and parametric dynamical systems under sub-Gaussian Levy white-noise
2008
In this study stochastic analysis of non-linear dynamical systems under α-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of α-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with α/2- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function …
Delay-Range-Dependent Linear Matrix Inequality Approach to Quantized H∞ Control of Linear Systems with Network-Induced Delays and Norm-Bounded Uncert…
2010
This paper deals with a convex optimization approach to the problem of robust network-based H∞ control for linear systems connected over a common digital communication network with static quantizers. Both the polytopic and the norm-bounded uncertainties are taken into consideration separately. First, the effect of both the output quantization levels and the network conditions under static quantizers is investigated. Second, by introducing a descriptor technique, using a Lyapunov—Krasovskii functional and a suitable change of variables, new required sufficient conditions are established in terms of delay-range-dependent linear matrix inequalities for the existence of the desired network-bas…
Qualitative Theory of Differential Equations, Difference Equations, and Dynamic Equations on Time Scales
2016
We are pleased to present this special issue. This volume reflects an increasing interest in the analysis of qualitative behavior of solutions to differential equations, difference equations, and dynamic equations on time scales. Numerous applications arising in the engineering and natural sciences call for the development of new efficient methods and for the modification and refinement of known techniques that should be adjusted for the analysis of new classes of problems. The twofold goal of this special issue is to reflect both the state-of-the-art theoretical research and important recent advances in the solution of applied problems.
Robust control of uncertain multi-inventory systems via linear matrix inequality
2008
We consider a continuous time linear multi inventory system with unknown demands bounded within ellipsoids and controls bounded within ellipsoids or polytopes. We address the problem of "-stabilizing the inventory since this implies some reduction of the inventory costs. The main results are certain conditions under which "-stabilizability is possible through a saturated linear state feedback control. All the results are based on a Linear Matrix Inequalities (LMIs) approach and on some recent techniques for the modeling and analysis of polytopic systems with saturations.
External constraints on optimal control strategies in molecular orientation and photofragmentation: Role of zero-area fields
2013
We propose a new formulation of optimal and local control algorithms which enforces the constraint of time-integrated zero-area on the control field. The fulfillment of this requirement, crucial in many physical applications, is mathematically implemented by the introduction of a Lagrange multiplier aiming at penalizing the pulse area. This method allows to design a control field with an area as small as possible, while bringing the dynamical system close to the target state. We test the efficiency of this approach on two control purposes in molecular dynamics, namely, orientation and photodissociation.
OLS Identification of network topologies
2011
Abstract In many applications, it is important to derive information about the topology and the internal connections of more dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology. We cast the problem as the optimization of a cost function where a set of parameters are used to operate a trade-off between accuracy and complexity in the final model. The problem of reducing the complexity is addressed by fixing a certain degree of sparsity and finding the…
The structure of the moduli spaces of toric dynamical systems
2023
We consider complex-balanced mass-action systems, or toric dynamical systems. They are remarkably stable polynomial dynamical systems arising from reaction networks seen as Euclidean embedded graphs. We study the moduli spaces of toric dynamical systems, called the toric locus: given a reaction network, we are interested in the topological structure of the set of parameters giving rise to toric dynamical systems. First we show that the complex-balanced equilibria depend continuously on the parameter values. Using this result, we prove that the toric locus of any toric dynamical system is connected. In particular, we emphasize its product structure: it is homeomorphic to the product of the s…