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Relevant bibliographies by topics / Piecewise smooth system

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Academic literature on the topic 'Piecewise smooth system'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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Journal articles on the topic "Piecewise smooth system"

1

Li, Shuangbao, Wei Zhang, and Yuxin Hao. "Melnikov-Type Method for a Class of Discontinuous Planar Systems and Applications." International Journal of Bifurcation and Chaos 24, no. 02 (2014): 1450022. http://dx.doi.org/10.1142/s0218127414500229.

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In this paper, we extend the well-known Melnikov method for smooth systems to a class of periodic perturbed piecewise smooth planar system. We assume that the unperturbed system is a piecewise Hamiltonian system which possesses a piecewise smooth homoclinic solution transversally crossing the switching manifold. The Melnikov-type function is explicitly derived by using the Hamiltonian function to measure the distance of the perturbed stable and unstable manifolds. Finally, we apply the obtained results to study the chaotic dynamics of a concrete piecewise smooth system.

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Li, Yurong, Liping Yuan, and Zhengdong Du. "Bifurcation of Nonhyperbolic Limit Cycles in Piecewise Smooth Planar Systems with Finitely Many Zones." International Journal of Bifurcation and Chaos 27, no. 10 (2017): 1750162. http://dx.doi.org/10.1142/s0218127417501620.

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Like for smooth systems, it is very important to discuss the stability and bifurcation of limit cycles in a piecewise smooth planar system. Most of the previous works focus only on hyperbolic limit cycles. Few works have considered nonhyperbolic limit cycles. In fact, to date, no concrete examples of piecewise smooth planar system with nonhyperbolic limit cycles have been given in literature. In this paper, we consider for the first time the bifurcation of nonhyperbolic limit cycles in piecewise smooth planar systems with discontinuities on finitely many straight lines intersecting at the orig

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Li, Shuangbao, Wensai Ma, Wei Zhang, and Yuxin Hao. "Melnikov Method for a Class of Planar Hybrid Piecewise-Smooth Systems." International Journal of Bifurcation and Chaos 26, no. 02 (2016): 1650030. http://dx.doi.org/10.1142/s0218127416500309.

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In this paper, we extend the well-known Melnikov method for smooth systems to a class of periodic perturbed planar hybrid piecewise-smooth systems. In this class, the switching manifold is a straight line which divides the plane into two zones, and the dynamics in each zone is governed by a smooth system. When a trajectory reaches the separation line, then a reset map is applied instantaneously before entering the trajectory in the other zone. We assume that the unperturbed system is a piecewise Hamiltonian system which possesses a piecewise-smooth homoclinic solution transversally crossing th

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ZHUSUBALIYEV, ZHANYBAI T., EVGENIY A. SOUKHOTERIN, and ERIK MOSEKILDE. "BORDER-COLLISION BIFURCATIONS AND CHAOTIC OSCILLATIONS IN A PIECEWISE-SMOOTH DYNAMICAL SYSTEM." International Journal of Bifurcation and Chaos 11, no. 12 (2001): 2977–3001. http://dx.doi.org/10.1142/s0218127401003991.

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Many problems of engineering and applied science result in the consideration of piecewise-smooth dynamical systems. Examples are relay and pulse-width control systems, impact oscillators, power converters, and various electronic circuits with piecewise-smooth characteristics. The subject of investigation in the present paper is the dynamical model of a constant voltage converter which represents a three-dimensional piecewise-smooth system of nonautonomous differential equations. A specific type of phenomena that arise in the dynamics of piecewise-smooth systems are the so-called border-collisi

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Chen, Shuang, and Zhengdong Du. "Stability and Perturbations of Homoclinic Loops in a Class of Piecewise Smooth Systems." International Journal of Bifurcation and Chaos 25, no. 09 (2015): 1550114. http://dx.doi.org/10.1142/s021812741550114x.

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Like for smooth systems, a typical method to produce multiple limit cycles for a given piecewise smooth planar system is via homoclinic bifurcation. Previous works only focused on limit cycles that bifurcate from homoclinic orbits of piecewise-linear systems. In this paper, we consider for the first time the same problem for a class of general nonlinear piecewise smooth systems. By introducing the Dulac map in a small neighborhood of the hyperbolic saddle, we obtain the approximation of the Poincaré map for the nonsmooth homoclinic orbit. Then, we give conditions for the stability of the homoc

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Liang, Feng, and Dechang Wang. "Limit Cycle Bifurcations Near a Piecewise Smooth Generalized Homoclinic Loop with a Saddle-Fold Point." International Journal of Bifurcation and Chaos 27, no. 05 (2017): 1750071. http://dx.doi.org/10.1142/s0218127417500717.

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In this paper, we suppose that a planar piecewise Hamiltonian system, with a straight line of separation, has a piecewise generalized homoclinic loop passing through a Saddle-Fold point, and assume that there exists a family of piecewise smooth periodic orbits near the loop. By studying the asymptotic expansion of the first order Melnikov function corresponding to the period annulus, we obtain the formulas of the first six coefficients in the expansion, based on which, we provide a lower bound for the maximal number of limit cycles bifurcated from the period annulus. As applications, two concr

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Pi, Dingheng, and Shihong Xu. "Bifurcation Analysis of Planar Piecewise Smooth Systems with a Line of Discontinuity." International Journal of Bifurcation and Chaos 26, no. 06 (2016): 1650104. http://dx.doi.org/10.1142/s0218127416501042.

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In this paper, we consider bifurcations of a class of planar piecewise smooth differential systems constituted by a general linear system and a quadratic Hamiltonian system. The linear system has four parameters. When the parameters vary in different regions, the left linear system can have a saddle, a node or a focus. For each case, we provide a completely qualitative analysis of the dynamical behavior for this piecewise smooth system. Our results generalize and improve the results in this direction.

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Jeffrey, Mike R. "Hidden Degeneracies in Piecewise Smooth Dynamical Systems." International Journal of Bifurcation and Chaos 26, no. 05 (2016): 1650087. http://dx.doi.org/10.1142/s0218127416500875.

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When a flow suffers a discontinuity in its vector field at some switching surface, the flow can cross through or slide along the surface. Sliding along the switching surface can be understood as the flow along an invariant manifold inside a switching layer. It turns out that the usual method for finding sliding modes — the Filippov convex combination or Utkin equivalent control — results in a degeneracy in the switching layer whenever the flow is tangent to the switching surface from both sides. We derive the general result and analyze the simplest case here, where the flow curves parabolicall

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Kousaka, Takuji, Tetsushi Ueta, Yue Ma, and Hiroshi Kawakami. "Control of chaos in a piecewise smooth nonlinear system." Chaos, Solitons & Fractals 27, no. 4 (2006): 1019–25. http://dx.doi.org/10.1016/j.chaos.2005.04.068.

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Li, Gaolei, Yuan Yue, Jianhua Xie, and Celso Grebogi. "Multistability in a quasiperiodically forced piecewise smooth dynamical system." Communications in Nonlinear Science and Numerical Simulation 84 (May 2020): 105165. http://dx.doi.org/10.1016/j.cnsns.2019.105165.

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Dissertations / Theses on the topic "Piecewise smooth system"

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Kubin, Ingrid, and Laura Gardini. "On the significance of borders." WU Vienna University of Economics and Business, 2018. http://epub.wu.ac.at/6449/1/WP266.pdf.

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We propose a prototype model of market dynamics in which all functional relationships are linear. We take into account three borders, defined by linear functions, which are intrinsic to the economic reasoning: non-negativity of prices; downward rigidity of capacity (depreciation) and a capacity constraint for the production decision. Given the linear specification, the borders are the only source for the emerging of cyclical and more complex dynamics. In particular, we discuss centre bifurcations, border collision bifurcations and degenerate flip bifurcations - dynamic phenomena the occurrence

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Commendatore, Pasquale, Ingrid Kubin, and Iryna Sushko. "The impact of Brexit on trade patterns and industry location: a NEG analysis." WU Vienna University of Economics and Business, 2018. http://epub.wu.ac.at/6450/1/WP267.pdf.

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We explore the effects of Brexit on trade patterns and on the spatial distribution of industry between the United Kingdom and the European Union and within the EU. Our study adopts a new economic geography (NEG) perspective developing a linear model with three regions, the UK and two separated regions composing the EU. The 3-region framework and linear demands allow for different trade patterns. Two possible ante-Brexit situations are possible, depending on the interplay between local market size, local competition and trade costs: industrial agglomeration or dispersion. Considering a soft and

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Simpson, David J. W. "Bifurcations in piecewise-smooth, continuous systems." Connect to online resource, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3337155.

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Chen, Yaming. "Dynamical properties of piecewise-smooth stochastic models." Thesis, Queen Mary, University of London, 2014. http://qmro.qmul.ac.uk/xmlui/handle/123456789/9129.

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Piecewise-smooth stochastic systems are widely used in engineering science. However, the theory of these systems is only in its infancy. In this thesis, we take as an example the Brownian motion with dry friction to illustrate dynamical properties of these systems with respect to three interesting topics: (i) weak-noise approximations, (ii) first-passage time (FPT) problems and (iii) functionals of stochastic processes. Firstly, we investigate the validity and accuracy of weak-noise approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example

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Wong, Chi Hong. "Border collision bifurcations in piecewise smooth systems." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/border-collision-bifurcations-in-piecewise-smooth-systems(1f2b9467-2c95-471b-82af-993b99d858ab).html.

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Piecewise smooth maps appear as models of various physical, economical and other systems. In such maps bifurcations can occur when a fixed point or periodic orbit crosses or collides with the border between two regions of smooth behaviour as a system parameter is varied. These bifurcations have little analogue in standard bifurcation theory for smooth maps and are often more complex. They are now known as "border collision bifurcations". The classification of border collision bifurcations is only available for one-dimensional maps. For two and higher dimensional piecewise smooth maps the study

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Geffert, Paul Matthias. "Nonequilibrium dynamics of piecewise-smooth stochastic systems." Thesis, Queen Mary, University of London, 2018. http://qmro.qmul.ac.uk/xmlui/handle/123456789/46783.

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Piecewise-smooth stochastic systems have attracted a lot of interest in the last decades in engineering science and mathematics. Many investigations have focused only on one-dimensional problems. This thesis deals with simple two-dimensional piecewise-smooth stochastic systems in the absence of detailed balance. We investigate the simplest example of such a system, which is a pure dry friction model subjected to coloured Gaussian noise. The nite correlation time of the noise establishes an additional dimension in the phase space and gives rise to a non-vanishing probability current. Our invest

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Kubin, Ingrid, and Laura Gardini. "Border Collision Bifurcations in Boom and Bust Cycles." WU Vienna University of Economics and Business, 2012. http://epub.wu.ac.at/3490/1/wp137.pdf.

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Boom and bust cycles are widely documented in the literature on industry dynamics. Rigidities and delays in capacity adjustment in combination with bounded rational behavior have been identified as central driving forces. We construct a model that features only these two elements and we show that this is indeed sufficient to reproduce some stylized facts of a boom and bust cycle. The bifurcation diagrams summarizing the dynamic behavior reveal complex cycles and in particular also abrupt changes in the nature of these cycles. We apply new insights from the mathematical theory of piecewise smo

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Park, Youngmin. "Infinitesimal Phase Response Curves for Piecewise Smooth Dynamical Systems." Case Western Reserve University School of Graduate Studies / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=case1370643724.

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Hasouneh, Monther A. "Feedback control of border collision bifurcations in piecewise smooth systems." College Park, Md. : University of Maryland, 2003. http://hdl.handle.net/1903/311.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2003.<br>Thesis research directed by: Electrical Engineering. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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Homer, Martin Edward. "Bifurcations and dynamics of piecewise smooth dynamical systems of arbitrary dimension." Thesis, University of Bristol, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299271.

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Books on the topic "Piecewise smooth system"

1

Laurea, Mario di Bernardo, Alan R. Champneys, Christopher J. Budd, and Piotr Kowalczyk, eds. Piecewise-smooth Dynamical Systems. Springer London, 2008. http://dx.doi.org/10.1007/978-1-84628-708-4.

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Bifurcations in piecewise-smooth continuous systems. World Scientific, 2010.

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Erik, Mosekilde, ed. Bifurcations and chaos in piecewise-smooth dynamical systems. World Scientific, 2003.

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M, Di Bernardo, ed. Piecewise-smooth dynamical systems: Theory and applications. Springer Verlag, 2008.

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Bernardo, Mario, Chris Budd, Alan Richard Champneys, and Piotr Kowalczyk. Piecewise-smooth Dynamical Systems: Theory and Applications. Springer, 2010.

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Bernardo, M. di, C. J. Budd, P. Kowalczyk, and Alan Richard Champneys. Piecewise-smooth Dynamical Systems: Theory and Applications (Applied Mathematical Sciences). Springer, 2007.

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The Octagonal PETs. American Mathematical Society, 2014.

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Book chapters on the topic "Piecewise smooth system"

1

Navarro-López, Eva M., and Domingo Cortés. "Controller Parameters Selection Through Bifurcation Analysis in a Piecewise-Smooth System." In Hybrid Systems: Computation and Control. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-71493-4_73.

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Gardini, Laura, and Iryna Sushko. "Bifurcations in Smooth and Piecewise Smooth Noninvertible Maps." In Difference Equations, Discrete Dynamical Systems and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20016-9_4.

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Solodov, Michael V., and Benav F. Svaiter. "A Globally Convergent Inexact Newton Method for Systems of Monotone Equations." In Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-6388-1_18.

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Teixeira, Marco Antonio, and Otávio M. L. Gomide. "Generic Singularities of 3D Piecewise Smooth Dynamical Systems." In Advances in Mathematics and Applications. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94015-1_15.

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Berardi, Marco. "Piecewise Smooth Systems: Equilibrium Points and Application to Gene Regulatory Networks." In Computational Science and Its Applications – ICCSA 2014. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09153-2_47.

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Hutchinson, J. M., and C. Koch. "Reconstruction of Piecewise Smooth Surfaces Using Simple Analog and Hybrid Networks." In Order and Chaos in Nonlinear Physical Systems. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-2058-4_16.

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Ueta, Tetsushi, Tohru Kawabe, Guanrong Chen, and Hiroshi Kawakami. "Calculation and Control of Unstable Periodic Orbits in Piecewise Smooth Dynamical Systems." In Chaos Control. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-44986-7_14.

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Martins, Ricardo M., and Durval J. Tonon. "The Chaotic Behavior of Piecewise Smooth Dynamical Systems on Torus and Sphere." In Trends in Mathematics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55642-0_22.

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Batenkov, D., and Y. Yomdin. "Local and Global Geometry of Prony Systems and Fourier Reconstruction of Piecewise-Smooth Functions." In Operator-Related Function Theory and Time-Frequency Analysis. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08557-9_2.

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Noel, Vincent, Sergei Vakulenko, and Ovidiu Radulescu. "Algorithm for Identification of Piecewise Smooth Hybrid Systems: Application to Eukaryotic Cell Cycle Regulation." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23038-7_20.

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Conference papers on the topic "Piecewise smooth system"

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Lauer, Fabien, and Gerard Bloch. "Piecewise smooth system identification in reproducing kernel Hilbert space." In 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE, 2014. http://dx.doi.org/10.1109/cdc.2014.7040408.

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Supeala, Valentin Stefan, Jean-Pierre Barbot, and Dan Alexandru Stoichescu. "Left invertibility of piecewise smooth system: The Alpazur case." In 2014 3rd International Symposium on Environmental Friendly Energies and Applications (EFEA). IEEE, 2014. http://dx.doi.org/10.1109/efea.2014.7059995.

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Vestroni, Fabrizio, Paolo Casini, and Oliviero Giannini. "Nonlinear Dynamics of Piecewise Smooth Systems and Damage Identification." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48901.

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This paper addresses the study of the nonlinear dynamics of non-smooth systems representative of beams with breathing cracks. The aim is to use the nonlinear characteristics of the system response to identify the damage in cracked structures that behave similarly to bilinear systems and hence exhibit nonlinear phenomena in the dynamic response even for low damage levels. The idea is supported by the study of a piecewise smooth 2-DOF model where a wide variety of nonlinear phenomena has been evidenced, which include among others the bifurcations of super-abundant modes and a number of resonance

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Luo, Albert C. J. "Grazing and Chaos in a Periodically Forced, Piecewise Linear System." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-59465.

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The criteria for the grazing bifurcation of a periodically forced, piecewise linear system are developed and the initial grazing manifolds are obtained. The grazing flows are illustrated. The mechanism for the fragmentation of the strange attractors caused by the grazing is discussed and the strange attractor fragmentized by grazing is illustrated through the Poincare mapping. This fragmentation phenomenon extensively exists in non-smooth dynamical systems.

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Fedonyuk, Vitaliy, and Phanindra Tallapragada. "The Stick-Slip Motion of a Chaplygin Sleigh With a Piecewise Smooth Nonholonomic Constraint." In ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/dscc2015-9820.

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The Chaplygin sleigh is a canonical problem of mechanical systems with nonholonomic constraints, which arises due to the role of friction. The motion of the cart has often been studied under the assumption that the magnitude of friction is as high as necessary to prevent slipping. We relax this assumption by setting a maximum finite value to the friction. The Chaplygin sleigh is then under a piecewise smooth nonholonomic constraint and transitions between ‘slip’ and ‘stick’ modes. We investigate these transitions and the resulting non smooth dynamics of the system. Further more the piecewise s

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Georgiadis, Fotios, Alexander F. Vakakis, D. Michael McFarland, and Lawrence Bergman. "Shock Isolation Through Passive Energy Pumping in a System With Piecewise Linear Stiffnesses." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48490.

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We investigate shock isolation designs based on nonlinear energy pumping caused by piecewise stiffness elements. In particular, we numerically study the shock isolation properties of a primary linear system of two coupled non-conservative oscillators with weakly coupled attachments possessing clearance nonlinearities. Under shock excitation the nonlinear attachments (termed nonlinear energy sinks – NESs) can be designed to absorb a significant portion of the input energy, thus enhancing the shock isolation performance of the primary system. In contrast to the classical linear vibration absorbe

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Menon, Santhosh, and Albert C. J. Luo. "An Analytical Prediction of the Global Period-1 Motion in a Periodically Forced, Piecewise Linear System." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48470.

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The analytical solution for the period-1 motion of a periodically forced piecewise linear system is obtained that based on the Poincare mapping and the switch planes pertaining to the two constraints. The stability and bifurcation of the period-1 motion are investigated, and numerical simulations are carried out to check the analytical prediction of period-1 motion. The symmetric and unsymmetrical stable period-1 motion plus an irregular motion are illustrated, and the analytical and numerical results are in a good agreement. This system demonstrates the behavior of the twin-well Duffing oscil

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Stahl, Patrick, and G. Nakhaie Jazar. "Frequency Response Analysis of Piecewise Nonlinear Vibration Isolator." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84879.

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Non-smooth piecewise functional isolators are smart passive vibration isolators that can provide effective isolation for high frequency/low amplitude excitation by introducing a soft primary suspension, and by preventing a high relative displacement in low frequency/high amplitude excitation by introducing a relatively damped secondary suspension. In this investigation a linear secondary suspension is attached to a nonlinear primary suspension. The primary is assumed to be nonlinear to model the inherent nonlinearities involved in real suspensions. However, the secondary suspension comes into

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Nguyen, Kim D., and Harry Dankowicz. "Principles of Dynamics for Design Applied to a Brush-Belt Material-Transfer System." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34431.

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This paper considers the performance characteristics of a brush-based material-transfer system, and the frictional interactions that result from the presence of particulate contaminants. The analysis of the dynamics of spherical objects transported through a cartridge by the brush is applied to isotropic and anisotropic belt designs. Experimental measurements of the load on individual objects, obtained using an instrumented cantilever, are compared with the predictions from a heuristic model, as well as preliminary observations from a qualitative bifurcation analysis of a piecewise-smooth dyna

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Ault, Holly K., and James C. Wilkinson. "Spline Based Design of Cam Contours for Improved Dynamic Performance." In ASME 1993 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/cie1993-0031.

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Abstract A method for the integrated design and manufacture of radial plate cams is discussed. Currently, a cam-follower system is designed by specifying constraints on the motion of the follower. The physical cam contour or cam pitch curve are not mathematically defined. The cam is manufactured from the discretized follower motion program. A new method for cam design is proposed which will produce a smooth, mathematically defined cam pitch curve while maintaining the proper constraints on the follower motion. Piecewise polynomial functions in the form of rational and/or non-rational splines m

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Reports on the topic "Piecewise smooth system"

1

Hassouneh, Munther A., and Eyad H. Abed. Lyapunov-Based Feedback Control of Border Collision Bifurcations in Piecewise Smooth Systems. Defense Technical Information Center, 2004. http://dx.doi.org/10.21236/ada439520.

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