scholarly journals FAMILIES OF SCROLL GRID ATTRACTORS

2002 ◽  
Vol 12 (01) ◽  
pp. 23-41 ◽  
Author(s):  
MÜŞTAK E. YALÇIN ◽  
JOHAN A. K. SUYKENS ◽  
JOOS VANDEWALLE ◽  
SERDAR ÖZOĞUZ
Keyword(s):  
State Space ◽  
Equilibrium Points ◽  
Strange Attractors ◽  
Current Feedback ◽  
Nonlinear Characteristics ◽  
State Variable ◽  
New Family ◽  
2D And 3D

In this paper a new family of scroll grid attractors is presented. These families are classified into three called 1D-, 2D- and 3D-grid scroll attractors depending on the location of the equilibrium points in state space. The scrolls generated from 1D-, 2D- and 3D-grid scroll attractors are located around the equilibrium points on a line, on a plane or in 3D, respectively. Due to the generalization of the nonlinear characteristics, it is possible to increase the number of scrolls in all state variable directions. A number of strange attractors from the scroll grid attractor families are presented. They have been experimentally verified using current feedback opamps. Also Lur'e representations are given for the scroll grid attractor families.

scholarly journals Characteristic phenomena in combustion

1997 ◽  
Vol 1 (2) ◽  
pp. 147-159
Author(s):  
Dirk Meinköhn
Keyword(s):  
State Space ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
The State ◽  
State Variable ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Singularity Order ◽  
The Relationship ◽  
Stable Stationary Solutions

For the case of a reaction–diffusion system, the stationary states may be represented by means of a state surface in a finite-dimensional state space. In the simplest example of a single semi-linear model equation given. in terms of a Fredholm operator, and under the assumption of a centre of symmetry, the state space is spanned by a single state variable and a number of independent control parameters, whereby the singularities in the set of stationary solutions are necessarily of the cuspoid type. Certain singularities among them represent critical states in that they form the boundaries of sheets of regular stable stationary solutions. Critical solutions provide ignition and extinction criteria, and thus are of particular physical interest. It is shown how a surface may be derived which is below the state surface at any location in state space. Its contours comprise singularities which correspond to similar singularities in the contours of the state surface, i.e., which are of the same singularity order. The relationship between corresponding singularities is in terms of lower bounds with respect to a certain distinguished control parameter associated with the name of Frank-Kamenetzkii.

The Dual State Variable Formulation as an Alternative to Perturbation Methods for the Analysis of Non-Linear Oscillators

2006 ◽  
Author(s):  
Alvin Post ◽  
Willem Stuiver
Keyword(s):  
State Space ◽  
Perturbation Methods ◽  
Duffing Oscillator ◽  
Van Der Pol Oscillator ◽  
Space Representation ◽  
Clear Understanding ◽  
Van Der Pol ◽  
State Space Representation ◽  
State Variable ◽  
Dimensional State Space

The "dual" state variable (DSV) formulation is a new way to represent ordinary differential equations. It is based on a framework that is consistent with the analysis of linear systems, and it allows the state space representation of a system to exhibit considerable symmetry. Its use in modeling requires a clear understanding of its unique four-dimensional state space, but it can be computationally simple. The DSV formulation has been successfully applied to model the nonlinear pendulum, the Duffing oscillator, and the van der Pol oscillator, with results that are superior to those of perturbation methods. An introduction to the DSV formulation and a framework for its systematic application as a modeling tool for nonlinear oscillators are presented.

scholarly journals Hybrid State Variable Incremental Integral for Reconstructing Extreme Multistability in Memristive Jerk System with Cubic Nonlinearity

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Mo Chen ◽  
Yang Feng ◽  
Han Bao ◽  
Bocheng Bao ◽  
Huagan Wu ◽  
...  
Keyword(s):  
Integral Transformation ◽  
Equilibrium Points ◽  
Mechanism Analysis ◽  
State Variables ◽  
Cubic Nonlinearity ◽  
Hybrid State ◽  
State Variable ◽  
Extreme Multistability ◽  
Memristive System ◽  
Jerk System

Memristive system with infinitely many equilibrium points has attracted much attention for the generation of extreme multistability, whose initial-dependent dynamics can be interpreted in a reduced-order model through incremental integral transformation of state variables. But, the memristive system with any extra nonlinear terms besides the memristor ones cannot be handled directly using this method. In addition, the transformed state variables could be divergent due to the asymmetry of the original system. To solve these problems, a hybrid state variable incremental integral (HSVII) method is proposed in this paper. With this method, the extreme multistability in a four-dimensional (4D) memristive jerk system with cubic nonlinearity is successfully reconstituted in a three-dimensional (3D) model and the divergent state variables are eliminated through ingenious linear state variable mapping. Thus, mechanism analysis and physical control of the special extreme multistability can readily be performed. A hardware circuit is finally designed and fabricated, and the theoretical and numerical results are verified by the experimental measurements. It is demonstrated that this HSVII method is effective for the analysis of multistable system with high-order nonlinearities.

scholarly journals A New Family of Chaotic Systems with Different Closed Curve Equilibrium

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 94 ◽  
Author(s):  
Xinhe Zhu ◽  
Wei-Shih Du
Keyword(s):  
Infinite Number ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Closed Curve ◽  
Phase Portraits ◽  
General Knowledge ◽  
Hidden Attractors ◽  
The Past ◽  
New Family ◽  
Dynamical Properties

Chaotic systems with hidden attractors, infinite number of equilibrium points and different closed curve equilibrium have received much attention in the past six years. In this work, we introduce a new family of chaotic systems with different closed curve equilibrium. Using the methods of equilibrium points, phase portraits, maximal Lyapunov exponents, Kaplan–Yorke dimension, and eigenvalues, we analyze the dynamical properties of the proposed systems and extend the general knowledge of such systems.

A new family of 1D, 2D and 3D frameworks aggregated from Ni5, Ni4 and Ni7 building units: synthesis, structure, and magnetism

2016 ◽  
Vol 45 (22) ◽  
pp. 9267-9278 ◽  
Author(s):  
Ya-Hui Liu ◽  
Li-Ping Lu ◽  
Miao-Li Zhu ◽  
Si-Si Feng ◽  
Feng Su
Keyword(s):  
Tricarboxylic Acid ◽  
Ferromagnetic Coupling ◽  
Magnetic Studies ◽  
3D Structures ◽  
New Family ◽  
Magnetic Chain ◽  
2D And 3D

Three polynuclear nickel(ii) complexes with 1D, 2D and 3D structures are controlled by carboxylate bridges of biphenyl-3,4′,5-tricarboxylic acid. Magnetic studies reveal that the polymers have ferromagnetic coupling features for 1 and 2 and an alternating magnetic chain behavior for 3.

Quantification of Numerical Stiffness for a Unified Viscoplastic Constitutive Model

1990 ◽  
Vol 112 (3) ◽  
pp. 271-276 ◽  
Author(s):  
S. M. Arnold
Keyword(s):  
Constitutive Model ◽  
State Space ◽  
Copper Alloy ◽  
Jacobian Matrix ◽  
The State ◽  
Maximum Difference ◽  
Material Parameters ◽  
State Variable ◽  
Variable Approach ◽  
State Point

Here the question of numerical stiffness pertaining to a unified viscoplastic constitutive model is examined. The viewpoint maintained throughout this study is the state variable approach. Stiffness is quantified by examining, analytically, the eigenvalues of the associated Jacobian matrix. Specific results, in the form of stiffness contours, for the material parameters characterizing the copper alloy NARloy-Z are presented in the associated uniaxial state space. The results indicate that the potential for numerical stiffness does exist, however the severity is highly dependent upon the location of the state point within the state space. Finally a qualitative analogy between the maximum difference in stiffness indicating eigenvalues and the G vectors of the corresponding state space is suggested.

scholarly journals Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and Experiments

Sensors ◽  
2020 ◽  
Vol 20 (23) ◽  
pp. 6738
Author(s):  
Santiago Rúa ◽  
Rafael E. Vásquez ◽  
Naveen Crasta ◽  
Carlos A. Zuluaga
Keyword(s):  
State Space ◽  
Equilibrium Points ◽  
High Gain ◽  
Observer Design ◽  
Luenberger Observer ◽  
State Space Realization ◽  
Observability Analysis ◽  
Space Realization ◽  
Tank System ◽  
Plant Configuration

This paper addresses the observability analysis and observer design for a nonlinear interacting three-tank system. The plant configuration is first described using the process and instrumentation diagram (P&ID) and a state–space realization is derived; some insights about the behavior of the nonlinear system, considering equilibrium points and the phase portrait are provided. Then, observability in the Hermann–Krener sense is analyzed. A high-gain observer (HGO) is then designed, using the equivalence of the original state–space realization with its observability canonical form, in order to guarantee convergence of the state estimation. The performance was validated through simulation and experiments in a multipurpose plant equipped with real sensors; the HGO response was compared to a Luenberger observer (for a linear approximation of the plant) and the Extended Kalman Filter (for which convergence is not guaranteed), considering nonlinearities, interaction, disturbances and noise. Theoretical and experimental results show that the HGO can provide robust estimation and disturbance rejection, despite the sensitivity of HGOs to noisy variables in processes such as level of liquids.

scholarly journals Reduction of second order linear dynamical systems, with large dissipation, by state variable transformations

1990 ◽  
Vol 32 (2) ◽  
pp. 207-222
Author(s):  
R. B. Leipnik
Keyword(s):  
Dynamical Systems ◽  
State Space ◽  
Computing Time ◽  
Square Root ◽  
Space Systems ◽  
Linear Dynamical Systems ◽  
State Variable ◽  
State Space Systems ◽  
Linear State ◽  
Eigenvectors And Eigenvalues

AbstractLinear dynamical systems of the Rayleigh form are transformed by linear state variable transformations , where A and B are chosen to simplify analysis and reduce computing time. In particular, A is essentially a square root of M, and B is a Lyapunov quotient of C by A. Neither K nor C is required to be symmetric, nor is C small. The resulting state-space systems are analysed by factorisation of the evolution matrices into reducible factors. Eigenvectors and eigenvalues are determined by these factors. Conditions for further simplification are derived in terms of Kronecker determinants. These results are compared with classical reductions of Rayleigh, Duncan, and Caughey, which are reviewed at the outset.

scholarly journals Modelling of an Esaki Tunnel Diode in a Circuit Simulator

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Nikhil M. Kriplani ◽  
Stephen Bowyer ◽  
Jennifer Huckaby ◽  
Michael B. Steer
Keyword(s):  
Mathematical Model ◽  
Intermediate State ◽  
Tunnel Diode ◽  
Nonlinear Characteristic ◽  
Nonlinear Characteristics ◽  
Circuit Simulator ◽  
Strongly Nonlinear ◽  
State Variable

A method for circuit-level modelling a physically realistic Esaki tunnel diode model is presented. A paramaterisation technique that transforms the strongly nonlinear characteristic of a tunnel diode into two relatively modest nonlinear characteristics is demonstrated. The introduction of an intermediate state variable results in a physically realistic mathematical model that is not only moderately nonlinear and therefore robust, but also single-valued.

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