Exploring branched Hamiltonians for a class of nonlinear systems

One of the less well-understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians resulting in multiple-valued Hamiltonians. We explore certain classes of branched Hamiltonians in the context of nonlinear autonomous differential equation of Liénard type. Two eligible elementary nonlinear models that emerge are shown to admit a feasible quantization along these lines.

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Green’s functional for a higher order ordinary integro-differential equation with nonlocal conditions

10.1063/1.4968454 ◽

2016 ◽

Author(s):

Kemal Özen

Keyword(s):

Differential Equation ◽

Nonlocal Conditions ◽

Higher Order ◽

Integro Differential Equation

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Asymptotic Dichotomy in a Class of Third-Order Nonlinear Differential Equations with Impulses

Abstract and Applied Analysis ◽

10.1155/2010/562634 ◽

2010 ◽

Vol 2010 ◽

pp. 1-20 ◽

Cited By ~ 1

Author(s):

Kun-Wen Wen ◽

Gen-Qiang Wang ◽

Sui Sun Cheng

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Nonlinear Differential Equation ◽

Nonlinear Differential Equations ◽

Functional Differential Equations ◽

Higher Order ◽

Third Order ◽

Order Nonlinear Differential Equation ◽

Functional Differential

Solutions of quite a few higher-order delay functional differential equations oscillate or converge to zero. In this paper, we obtain several such dichotomous criteria for a class of third-order nonlinear differential equation with impulses.

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$${L_\infty }$$ Fault Estimation and Fault-Tolerant Control for Nonlinear Systems by T–S Fuzzy Model Method with Local Nonlinear Models

International Journal of Fuzzy Systems ◽

10.1007/s40815-021-01061-6 ◽

2021 ◽

Author(s):

Yang Wang ◽

Tieshan Li ◽

Yue Wu ◽

Ximing Yang ◽

C. L. Philip Chen ◽

...

Keyword(s):

Nonlinear Systems ◽

Fault Tolerant ◽

Nonlinear Models ◽

Fuzzy Model ◽

Fault Tolerant Control ◽

Fault Estimation ◽

Model Method

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Duality of Complex Systems Built from Higher-Order Elements

Complexity ◽

10.1155/2018/5719397 ◽

2018 ◽

Vol 2018 ◽

pp. 1-15 ◽

Cited By ~ 7

Author(s):

Dalibor Biolek ◽

Zdeněk Biolek ◽

Viera Biolková

Keyword(s):

Nonlinear Systems ◽

Complex Systems ◽

Higher Order ◽

Duality Principle ◽

Shift Type ◽

Hardware Emulation ◽

Classical Duality ◽

Memristive Circuits ◽

Circuit Elements

The duality of nonlinear systems built from higher-order two-terminal Chua’s elements and independent voltage and current sources is analyzed. Two different approaches are now being generalized for circuits with higher-order elements: the classical duality principle, hitherto restricted to circuits built from R-C-L elements, and Chua’s duality of memristive circuits. The so-called storeyed structure of fundamental elements is used as an integrating platform of both approaches. It is shown that the combination of associated flip-type and shift-type transformations of the circuit elements can generate dual networks with interesting features. The regularities of the duality can be used for modeling, hardware emulation, or synthesis of systems built from elements that are not commonly available, such as memristors, via classical dual elements.

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Output tracking controller design for MIMO nonlinear systems with higher-order and unmatched uncertainties

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187) ◽

10.1109/cdc.2000.912038 ◽

2002 ◽

Cited By ~ 2

Author(s):

Chiang-Cheng Chiang ◽

Zu-Hung Kuo

Keyword(s):

Nonlinear Systems ◽

Controller Design ◽

Higher Order ◽

Mimo Nonlinear Systems ◽

Output Tracking ◽

Tracking Controller ◽

Unmatched Uncertainties

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New Properties of Modified Second Kind Chebyshev Polynomials

Journal of Southwest Jiaotong University ◽

10.35741/issn.0258-2724.55.3.2 ◽

2020 ◽

Vol 55 (3) ◽

Author(s):

Semaa Hassan Aziz ◽

Mohammed Rasheed ◽

Suha Shihab

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Chebyshev Polynomial ◽

Chebyshev Polynomials ◽

Digital Computer ◽

Higher Order ◽

Algebraic Equations ◽

Equation Problem ◽

Higher Order Differential Equations

Modified second kind Chebyshev polynomials for solving higher order differential equations are presented in this paper. This technique, along with some new properties of such polynomials, will reduce the original differential equation problem to the solution of algebraic equations with a straightforward and computational digital computer. Some illustrative examples are included. The modified second kind Chebyshev polynomial is calculated using only a small number of the modified second kind Chebyshev polynomials, which leads to attractive results.

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A Study of Nonlinear Boundary Value Problem

10.5772/intechopen.100491 ◽

2021 ◽

Author(s):

Noureddine Bouteraa ◽

Habib Djourdem

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Iterative Method ◽

Boundary Value Problem ◽

Higher Order ◽

Nonlinear Boundary Value Problem ◽

Point Boundary ◽

Error Estimations ◽

Fractional Differential

In this chapter, firstly we apply the iterative method to establish the existence of the positive solution for a type of nonlinear singular higher-order fractional differential equation with fractional multi-point boundary conditions. Explicit iterative sequences are given to approximate the solutions and the error estimations are also given. Secondly, we cover the multi-valued case of our problem. We investigate it for nonconvex compact valued multifunctions via a fixed point theorem for multivalued maps due to Covitz and Nadler. Two illustrative examples are presented at the end to illustrate the validity of our results.

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