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Largest Lyapunov Exponents and Bifurcations of Stochastic Nonlinear Systems
Shock and Vibration, 1996 Two commonly adopted expressions for the largest Lyapunov exponents of linearized stochastic systems are reviewed. Their features are discussed in light of bifurcation analysis and one expression is selected for evaluating the largest Lyapunov exponent ...
C.W.S. To, D.M. Li
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Can the Flap of a Butterfly’s Wings Shift a Tornado into Texas—Without Chaos?
Atmosphere, 2023 In our title, “chaos” means there is a positive Lyapunov exponent that causes the tornado to move. We are asserting that a positive Lyapunov exponent is not always needed to have a butterfly effect.
Yoshitaka Saiki, James A. Yorke
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International Journal of Mechanical System Dynamics, EarlyView.ABSTRACT Fractional calculus, with its unique advantage in describing memory and nonlocal effects, has become a key tool for modeling nonlinear dynamic systems. Its integration with circuit systems has opened up a new paradigm for modern circuit design.
Zhimo Jian +4 more
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Adaptive Sliding‐Mode Control of a Perturbed Diffusion Process With Pointwise In‐Domain Actuation
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT A sliding mode–based adaptive control law is proposed for a class of diffusion processes featuring a spatially‐varying uncertain diffusivity and equipped with several point‐wise actuators located at the two boundaries of the spatial domain as well as in its interior.
Paul Mayr +3 more
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Optimal Homogeneous ℒp$$ {\boldsymbol{\mathcal{L}}}_{\boldsymbol{p}} $$‐Gain Controller
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT Nonlinear ℋ∞$$ {\mathscr{H}}_{\infty } $$‐controllers are designed for arbitrarily weighted, continuous homogeneous systems with a focus on systems affine in the control input. Based on the homogeneous ℒp$$ {\mathcal{L}}_p $$‐norm, the input–output behavior is quantified in terms of the homogeneous ℒp$$ {\mathcal{L}}_p $$‐gain as a ...
Daipeng Zhang +3 more
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Studying Transition Behavior of Neutron Point Kinetics Equations Using the Lyapunov Exponent Method [PDF]
Journal of Sciences, Islamic Republic of Iran, 2016 The neutron density is one of the most important dynamical parameters in a reactor. It is directly related to the control and stability of the reactor power. Any change in applied reactivity and some of dynamical parameters in the reactor causes a change
M. Seidi, R. Khodabakhsh, S. Behnia
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Predicting Traffic Flow in Local Area Networks by the Largest Lyapunov Exponent
Entropy, 2016 The dynamics of network traffic are complex and nonlinear, and chaotic behaviors and their prediction, which play an important role in local area networks (LANs), are studied in detail, using the largest Lyapunov exponent.
Yan Liu, Jiazhong Zhang
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International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT This paper establishes an implementation‐aware framework for Barrier Function Adaptation (BFA) and shows that discrete‐time realizations fundamentally alter the logic of final‐set adjustment. In particular, sufficient conditions are derived to preserve the key benefits of BFA (predefined performance, gain adaptation with uncertain perturbation
Luis Ovalle +3 more
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Exact Robust Filtering and Differentiation Based on Sliding Modes and Homogeneity
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT This article addresses the problem of online estimation of the derivatives of a signal corrupted by measurement noise. The measured signal is modeled as the sum of a smooth nominal component and a uniformly bounded noise term. A key objective is to attenuate the effect of high‐frequency noise.
Jaime A. Moreno, Arie Levant
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Stability analysis of fuzzy controllers through the computation of the Lyapunov Exponent
Revista Iberoamericana de Automática e Informática Industrial RIAI, 2015 In order to design and implement any type of controller, their stability analysis is pivotal. At this regard, Lyapunov's analytical method consists in finding a candidate function as a sufficient but not necessary condition to validate the stability of ...
Leonardo Alonso Martínez Rivera +2 more
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