Search results for "Stability"
showing 10 items of 3085 documents
Hidden attractors in dynamical systems
2016
Complex dynamical systems, ranging from the climate, ecosystems to financial markets and engineering applications typically have many coexisting attractors. This property of the system is called multistability. The final state, i.e., the attractor on which the multistable system evolves strongly depends on the initial conditions. Additionally, such systems are very sensitive towards noise and system parameters so a sudden shift to a contrasting regime may occur. To understand the dynamics of these systems one has to identify all possible attractors and their basins of attraction. Recently, it has been shown that multistability is connected with the occurrence of unpredictable attractors whi…
Nonlinear optical properties of low molecular organic glasses formed by triphenyl modified chromophores
2012
The series of organic molecular glasses have been studied as possible candidates for nonlinear optical (NLO) applications. Amorphous phase formation of investigated materials is ensured by the presence of bulky triphenyl substituents in molecular structure of NLO chromophores. Linear optical properties as well as NLO coefficients and thermal stability of NLO activity for the 13 molecular materials in glassy thin solid films have been determined. For the benzylidene-1,3-indandione chromophore containing compound the highest d33 value equal to 280 pm/V was measured under the 1064 nm excitation. Among the investigated compounds uppermost achieved thermal sustainability of NLO response was 108 …
Nonlinear higher-order polariton topological insulator
2020
We address the resonant response and bistability of the exciton-polariton corner states in a higher-order nonlinear topological insulator realized with kagome arrangement of microcavity pillars. Such states are resonantly excited and exist due to the balance between pump and losses, on the one hand, and between nonlinearity and dispersion in inhomogeneous potential landscape, on the other hand, for pump energy around eigen-energies of corresponding linear localized modes. Localization of the nonlinear corner states in a higher-order topological insulator can be efficiently controlled by tuning pump energy. We link the mechanism of corner state formation with symmetry of the truncated kagome…
Improving the stability bound for the PPH nonlinear subdivision scheme for data coming from strictly convex functions
2021
Abstract Subdivision schemes are widely used in the generation of curves and surfaces, and therefore they are applied in a variety of interesting applications from geological reconstructions of unaccessible regions to cartoon film productions or car and ship manufacturing. In most cases dealing with a convexity preserving subdivision scheme is needed to accurately reproduce the required surfaces. Stability respect to the initial input data is also crucial in applications. The so called PPH nonlinear subdivision scheme is proven to be both convexity preserving and stable. The tighter the stability bound the better controlled is the final output error. In this article a more accurate stabilit…
Non-fragile fuzzy control design for nonlinear time-delay systems
2013
In this paper, a non-fragile fuzzy control design is proposed for a class of nonlinear systems with mixed discrete and distributed time delays. The Takagi and Sugeno (T-S) fuzzy set approach is applied to the modelling of the nonlinear dynamics, and a T-S fuzzy model is constructed, which can represent the nonlinear system. Then, based on the fuzzy linear model, a fuzzy linear controller is developed to stabilize the nonlinear system. The control law is obtained to ensure stochastically exponentially stability in the mean square. The sufficient conditions for the existence of such a control are proposed in terms of certain linear matrix inequalities.
Efficiency and Stability of a Family of Iterative Schemes for Solving Nonlinear Equations
2019
In this paper, we construct a family of iterative methods with memory from one without memory, analyzing their convergence and stability. The main aim of this manuscript yields in the advantage that the use of real multidimensional dynamics gives us to decide among the different classes designed and, afterwards, to select its most stable members. Some numerical tests confirm the theoretical results.
Entropy dissipation of moving mesh adaptation
2014
Non-uniform grids and mesh adaptation have become an important part of numerical approximations of differential equations over the past decades. It has been experimentally noted that mesh adaptation leads not only to locally improved solution but also to numerical stability of the underlying method. In this paper we consider nonlinear conservation laws and provide a method to perform the analysis of the moving mesh adaptation method, including both the mesh reconstruction and evolution of the solution. We moreover employ this method to extract sufficient conditions — on the adaptation of the mesh — that stabilize a numerical scheme in the sense of the entropy dissipation.
Convergence analysis of cubature Kalman filter
2014
This paper investigates the stability analysis of cubature Kalman filter (CKF) for nonlinear systems with linear measurement. The certain conditions to ensure that the estimation error of CKF remains bounded are proved. Then, the effect of process noise covariance is investigated and an adaptive process noise covariance is proposed to deal with large estimation error. Accordingly, a modified CKF (MCKF) is developed to enhance the stability and accuracy of state estimation. The performance of the MCKF is compared to the CKF by two case studies. Simulation results demonstrate that the large estimation error may lead to instability of CKF while the MCKF is successfully able to estimate the sta…
Small-gain conditions for stochastic network systems
2013
In this paper, some small-gain conditions are presented for stochastic network systems which can describe many large-scale systems with interconnections, nonlinear behaviors, uncertainties and random disturbances. One subsystem is selected as monitor with the requirement that the gains to other systems are smooth concave functions. The relations of members under the supervise of the monitor are described as bilateral plus multilateral relations of gains. For the deterministic case, the requirement on the monitor can be removed. To demonstrate the power of this result, the small-gain conditions cover interconnected system with two subsystems as a special case. Compared with the existing resu…
Stabilization for a class of nonlinear networked control systems via polynomial fuzzy model approach
2014
This article is concerned with the stabilization problem for nonlinear networked control systems which are represented by polynomial fuzzy models. Two communication features including signal transmission delays and data missing are taken into account in a network environment. To solve the network-induced communication problems, a novel sampled-data fuzzy controller is designed to guarantee that the closed-loop system is asymptotically stable. The stability and stabilization conditions are presented in terms of sum of squares SOS, which can be numerically solved via SOSTOOLS. Finally, a simulation example is provided to demonstrate the feasibility of the proposed method. © 2014 Wiley Periodi…