Stochastic Sensitivity Analysis and Noise-Induced Chaos in 2D Logistic-Type Model

We study the dynamics of stochastically forced 2D logistic-type discrete model. Under random disturbances, stochastic trajectories leaving deterministic attractors can form complex dynamic regimes that have no analogue in the deterministic case. In this paper, we analyze an impact of the random noise on 2D logistic-type model in the bistability zones with coexisting attractors (equilibria, closed invariant curves, discrete cycles). For the constructive probabilistic analysis of the random states distribution around such attractors, a stochastic sensitivity functions technique and method of confidence domains are used. For the considered model, on the base of the suggested approach, a phenomenon of noise-induced transitions between attractors and the generation of chaos are analyzed.

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Stochastic Phenomena in One-Dimensional Rulkov Model of Neuronal Dynamics

Discrete Dynamics in Nature and Society ◽

10.1155/2015/495417 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7 ◽

Cited By ~ 6

Author(s):

Irina Bashkirtseva

Keyword(s):

Period Doubling ◽

Neuronal Dynamics ◽

One Dimensional ◽

Sensitivity Functions ◽

Stochastic Sensitivity ◽

Random Disturbances ◽

Transient Zone ◽

Stochastic Regimes ◽

Stochastic Phenomena ◽

Stochastic Bifurcations

We study the nonlinear Rulkov map-based neuron model forced by random disturbances. For this model, an overview of the variety of stochastic regimes is given. For the parametric analysis of these regimes, the stochastic sensitivity functions technique is used. In a period-doubling zone, we analyze backward stochastic bifurcations modelling changes of modality of noisy neuron spiking. Noise-induced transitions in a zone of bistability are considered. It is shown how such random transitions can generate a new neuronal regime of the stochastic bursting and transfer the system from order to chaos. A transient zone of values of noise intensity corresponding to the onset of noise-induced bursting and chaotization is localized by the stochastic sensitivity functions technique.

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Optimal Data-Driven Modeling-Free Differential-Inversion-Based Iterative Control: A Wafer Stage Example

Volume 2: Intelligent Transportation/Vehicles; Manufacturing; Mechatronics; Engine/After-Treatment Systems; Soft Actuators/Manipulators; Modeling/Validation; Motion/Vibration Control Applications; Multi-Agent/Networked Systems; Path Planning/Motion Control; Renewable/Smart Energy Systems; Security/Privacy of Cyber-Physical Systems; Sensors/Actuators; Tracking Control Systems; Unmanned Ground/Aerial Vehicles; Vehicle Dynamics, Estimation, Control; Vibration/Control Systems; Vibrations ◽

10.1115/dscc2020-3281 ◽

2020 ◽

Author(s):

Zezhou Zhang ◽

Qingze Zou

Keyword(s):

System Dynamics ◽

High Performance ◽

Random Noise ◽

High Accuracy ◽

Data Driven ◽

Modeling Process ◽

Random Disturbances ◽

Noise Disturbances ◽

Data Driven Modeling ◽

Iterative Control

Abstract In this paper, an optimal data-driven modeling-free differential-inversion-based iterative control (OMFDIIC) method is proposed for both high performance and robustness in the presence of random disturbances. Achieving high accuracy and fast convergence is challenging as the system dynamics behaviors vary due to the external uncertainties and the system bandwidth is limited. The aim of the proposed method is to compensate for the dynamics effect without modeling process and achieve both high accuracy and robust convergence, by extending the existed modeling-free differential-inversion-based iterative control (MFDIIC) method through a frequency- and iteration-dependent gain. The convergence of the OMFDIIC method is analyzed with random noise/disturbances considered. The developed method is applied to a wafer stage, and shows a significant improvement in the performance.

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