scholarly journals Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Ricardo Aguilar-López ◽  
Rafael Martínez-Guerra ◽  
Juan L. Mata-Machuca
Keyword(s):  
Numerical Experiments ◽  
Bounded Function ◽  
Initial Conditions ◽  
Integral Form ◽  
Synchronization Error ◽  
Nonlinear Observer ◽  
Chaotic Oscillators ◽  
Benchmark Model ◽  
Satisfactory Performance ◽  
Asymptotic Synchronization

The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves’ oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.

scholarly journals A New Finite-Time Observer for Nonlinear Systems: Applications to Synchronization of Lorenz-Like Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Ricardo Aguilar-López ◽  
Juan L. Mata-Machuca
Keyword(s):  
Nonlinear Systems ◽  
Control Theory ◽  
Finite Time ◽  
Numerical Experiments ◽  
Time Synchronization ◽  
Upper Bounds ◽  
Observer Design ◽  
Synchronization Error ◽  
Chaotic Oscillator ◽  
Chaotic Oscillators

This paper proposes a synchronization methodology of two chaotic oscillators under the framework of identical synchronization and master-slave configuration. The proposed methodology is based on state observer design under the frame of control theory; the observer structure provides finite-time synchronization convergence by cancelling the upper bounds of the main nonlinearities of the chaotic oscillator. The above is showed via an analysis of the dynamic of the so called synchronization error. Numerical experiments corroborate the satisfactory results of the proposed scheme.

scholarly journals Rotational Behavior of Cometary-type Bodies

1992 ◽  
Vol 152 ◽  
pp. 291-296
Author(s):  
Eric Bois ◽  
Pascal Oberti ◽  
Claude Froeschlé
Keyword(s):  
Qualitative Study ◽  
Rotational Motion ◽  
Numerical Experiments ◽  
Initial Conditions ◽  
Close Approach ◽  
Rotational Behavior ◽  
Comet Nucleus ◽  
Gravitational Perturbation ◽  
The Sun ◽  
Sensitivity To Initial Conditions

The present paper deals with a general dynamical qualitative study of the rotational motion for cometary-type bodies submitted to gravitational torques. Numerical experiments of the evolution of comet nucleus attitude have been then performed, including the Sun and Jupiter's disturbing torques in the model. Results show small effects of the solar gravitational perturbation for Halley-type orbits. Only a very close-approach with Jupiter induces notable effects. The latter configuration presents some interesting sensitivity to initial conditions.

scholarly journals PEDESTRIAN FLOW MODELS WITH SLOWDOWN INTERACTIONS

2013 ◽  
Vol 24 (02) ◽  
pp. 249-275 ◽  
Author(s):  
ALINA CHERTOCK ◽  
ALEXANDER KURGANOV ◽  
ANTHONY POLIZZI ◽  
ILYA TIMOFEYEV
Keyword(s):  
Numerical Experiments ◽  
Initial Conditions ◽  
Coupled System ◽  
Coarse Grained ◽  
Order System ◽  
Stochastic Cellular Automata ◽  
Cellular Automata Model ◽  
Flow Models ◽  
Pedestrian Traffic ◽  
Microscopic Stochastic Model

In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for pedestrians moving in two opposite directions. Coarse-grained mesoscopic and macroscopic analogs are derived leading to the coupled system of PDEs for the density of the pedestrian traffic. The obtained first-order system of conservation laws is only conditionally hyperbolic. We also derive higher-order nonlinear diffusive corrections resulting in a parabolic macroscopic PDE model. Numerical experiments comparing and contrasting the behavior of the microscopic stochastic model and the resulting coarse-grained PDEs for various parameter settings and initial conditions are performed. These numerical experiments demonstrate that the nonlinear diffusion is essential for reproducing the behavior of the stochastic system in the nonhyperbolic regime.

scholarly journals Numerical Experiments on the Motion of the Outer Planets

1992 ◽  
Vol 152 ◽  
pp. 25-32 ◽  
Author(s):  
Gerald D. Quinlan
Keyword(s):  
Lyapunov Exponent ◽  
Solar System ◽  
Probability Distribution ◽  
Numerical Experiments ◽  
Initial Conditions ◽  
Major Axis ◽  
Solar Systems ◽  
Outer Planets ◽  
System A ◽  
Real Value

We have integrated the motion of the four Jovian planets on Myr timescales in fictitious solar systems in which the orbits differ from those of the real solar system. A change of ≲1% in the major axis of any one of the planets from its real value can lead to chaotic motion with a Lyapunov exponent larger than 10-5 yr−1. A survey of fifty solar systems with initial conditions chosen at random from a reasonable probability distribution shows the majority of them to be chaotic.

Message Embedded Chaotic Masking Synchronization Scheme Based on the Generalized Lorenz System and Its Security Analysis

2016 ◽  
Vol 26 (08) ◽  
pp. 1650140 ◽  
Author(s):  
Sergej Čelikovský ◽  
Volodymyr Lynnyk
Keyword(s):  
Numerical Experiments ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Bounded Function ◽  
Security Analysis ◽  
Encryption Scheme ◽  
The Novel ◽  
Generalized Lorenz System ◽  
Synchronization Signal ◽  
Synchronization Scheme

This paper focuses on the design of the novel chaotic masking scheme via message embedded synchronization. A general class of the systems allowing the message embedded synchronization is presented here, moreover, it is shown that the generalized Lorenz system belongs to this class. Furthermore, the secure encryption scheme based on the message embedded synchronization is proposed. This scheme injects the embedded message into the dynamics of the transmitter as well, ensuring thereby synchronization with theoretically zero synchronization error. To ensure the security, the embedded message is a sum of the message and arbitrary bounded function of the internal transmitter states that is independent of the scalar synchronization signal. The hexadecimal alphabet will be used to form a ciphertext making chaotic dynamics of the transmitter even more complicated in comparison with the transmitter influenced just by the binary step-like function. All mentioned results and their security are tested and demonstrated by numerical experiments.

Pascal's recurrence relation and even-aged-forest stand dynamics

1992 ◽  
Vol 22 (12) ◽  
pp. 1996-1999
Author(s):  
Rolfe A. Leary ◽  
Hien Phan ◽  
Kevin Nimerfro
Keyword(s):  
Differential Equation ◽  
Relative Density ◽  
Closed Form ◽  
Initial Conditions ◽  
Closed Form Solution ◽  
Integral Form ◽  
Forest Stand ◽  
Form Solution ◽  
Density Change ◽  
Stand Dynamics

A common method of modelling forest stand dynamics is to use permanent growth plot remeasurements to calibrate a whole-stand growth model expressed as an ordinary differential equation. To obtain an estimate of future conditions, either the differential equation is integrated numerically or, if analytic, the differential equation is solved in closed form. In the latter case, a future condition is obtained simply by evaluating the integral form for the age of interest, subject to appropriate initial conditions. An older method of modelling forest stand dynamics was to use a normal or near-normal yield table as a density standard and calibrate a relative density change equation from permanent plot remeasurements. An estimate of a future stand property could be obtained by iterating from a known initial relative density. In this paper we show that when the relative density change equation has a particular form, the historical method also has a closed form solution, given by a sequence of polynomials with coefficients from successive rows of Pascal's arithmetic triangle.

scholarly journals Properties of self-gravitating quasi-stationary states

2020 ◽  
Vol 643 ◽  
pp. A118
Author(s):  
Francesco Sylos Labini ◽  
Roberto Capuzzo-Dolcetta
Keyword(s):  
Density Profile ◽  
Numerical Experiments ◽  
Energy Exchange ◽  
Initial Conditions ◽  
Initial Density ◽  
Density Fluctuations ◽  
Quasi Equilibrium ◽  
Stationary States ◽  
Top Down ◽  
Bottom Up

Initially far out-of-equilibrium, self-gravitating systems form quasi-stationary states (QSS) through a collisionless relaxation dynamics. These may arise from a bottom-up aggregation of structures or in a top-down frame; their quasi-equilibrium properties are well described by the Jeans equation and are not universal. These QSS depend on initial conditions. To understand the origin of such dependence, we present the results of numerical experiments of initially cold and spherical systems characterized by various choices of the spectrum of initial density fluctuations. The amplitude of such fluctuations determines whether the system relaxes in a top-down or bottom-up manner. We find that statistical properties of the resulting QSS mainly depend upon the amount of energy exchanged during the formation process. In particular, in the violent top-down collapses the energy exchange is large and the QSS show an inner core with an almost flat density profile and a quasi Maxwell-Boltzmann (isotropic) velocity distribution, while their outer regions display a density profile ρ(r) ∝ r−α (α >  0) with radially elongated orbits. We show analytically that α = 4, in agreement with numerical experiments. In the less violent bottom-up dynamics, the energy exchange is much smaller, the orbits are less elongated, and 0 < α(r) ≤ 4, where the density profile is well fitted by the Navarro-Frenk-White behavior. Such a dynamical evolution is shown by both nonuniform spherical isolated systems and by halos extracted from cosmological simulations. We consider the relation of these results with the core-cusp problem and conclude that this can be solved naturally if galaxies form through a monolithic collapse.

scholarly journals Estimation of oscillation velocities of oscillator network

2018 ◽  
Vol 32 ◽  
pp. 182-189
Author(s):  
Volodymyr Shcherbak ◽  
Iryna Dmytryshyn
Keyword(s):  
Dynamical System ◽  
Nonlinear Oscillations ◽  
Initial Conditions ◽  
Nonlinear Dynamical System ◽  
Stable Limit Cycle ◽  
Nonlinear Observer ◽  
Stable Limit ◽  
Nonlinear Dynamical ◽  
Biomechanical Models ◽  
Neural Ensembles

The study of the collective behavior of multiscale dynamic processes is currently one of the most urgent problems of nonlinear dynamics. Such systems arise on modelling of many cyclical biological or physical processes. It is of fundamental importance for understanding the basic laws of synchronous dynamics of distributed active subsystems with oscillations, such as neural ensembles, biomechanical models of cardiac or locomotor activity, models of turbulent media, etc. Since the nonlinear oscillations that are observed in such systems have a stable limit cycle , which does not depend on the initial conditions, then a system of interconnected nonlinear oscillators is usually used as a model of multiscale processes. The equations of Lienar type are often used as the main dynamic model of each of these oscillators. In a number of practical control problems of such interconnected oscillators it is necessary to determine the oscillation velocities by known data. This problem is considered as observation problem for nonlinear dynamical system. A new method – a synthesis of invariant relations is used to design a nonlinear observer. The method allows us to represent unknowns as a function of known quantities. The scheme of the construction of invariant relations consists in the expansion of the original dynamical system by equations of some controlled subsystem (integrator). Control in the additional system is used for the synthesis of some relations that are invariant for the extended system and have the attraction property for all of its trajectories. Such relations are considered in observation problems as additional equations for unknown state vector of initial oscillators ensemble. To design the observer, first we introduce a observer for unique oscillator of Lienar type and prove its exponential convergence. This observer is then extended on several coupled Lienar type oscillators. The performance of the proposed method is investigated by numerical simulations.

scholarly journals Climate noise effect on uncertainty of hydrological extremes: numerical experiments with hydrological and climate models

2015 ◽  
Vol 369 ◽  
pp. 49-53 ◽  
Author(s):  
A. N. Gelfan ◽  
V. A. Semenov ◽  
Yu. G. Motovilov
Keyword(s):  
Numerical Experiments ◽  
Climate Models ◽  
Hydrological Model ◽  
Climate Model ◽  
Initial Conditions ◽  
Hydrological Regime ◽  
Internal Variability ◽  
Climate Impact ◽  
Noise Effect ◽  
Climate Noise

Abstract. An approach has been proposed to analyze the simulated hydrological extreme uncertainty related to the internal variability of the atmosphere ("climate noise"), which is inherent to the climate system and considered as the lowest level of uncertainty achievable in climate impact studies. To assess the climate noise effect, numerical experiments were made with climate model ECHAM5 and hydrological model ECOMAG. The case study was carried out to Northern Dvina River basin (catchment area is 360 000 km2), whose hydrological regime is characterised by extreme freshets during spring-summer snowmelt period. The climate noise was represented by ensemble ECHAM5 simulations (45 ensemble members) with identical historical boundary forcing and varying initial conditions. An ensemble of the ECHAM5-outputs for the period of 1979–2012 was used (after bias correction post-processing) as the hydrological model inputs, and the corresponding ensemble of 45 multi-year hydrographs was simulated. From this ensemble, we derived flood statistic uncertainty caused by the internal variability of the atmosphere.

scholarly journals State variables monitoring using a class of nonlinear observer based estimator, applied to continuous bio-system

2008 ◽  
Vol 6 (03) ◽  
Author(s):  
Ricardo Aguilar-López ◽  
Ricardo Acevedo-Gómez ◽  
Marí­a Isabel Neria González ◽  
Alma Rosa Domí­nguez-Bocanegra
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Nonlinear Observer ◽  
Kinetic Term ◽  
State Variables ◽  
State Estimator ◽  
Sulfate Reducing ◽  
Satisfactory Performance ◽  
Key Variables ◽  
Nonlinear State

In this work, the state estimation of key variables such as biomass and products of a sulfate reducing bacterium is predicted by using only sulfate (substrate) concentration measurements under the assumption of an unknown kinetic term. The process was developed by  ontinuous culture, where the mathematical kinetic model for the biomass, sulfate and sulfide concentrations is presented and tuned using experimental data. The design of the nonlinear state estimator takes into account an adaptive gain. The results of the proposed estimation methodology were generated via numerical simulation; they showed a satisfactory performance.

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