scholarly journals A general framework for boundary equilibrium bifurcations of Filippov systems

2018 ◽  
Vol 28 (10) ◽  
pp. 103114 ◽  
Author(s):  
D. J. W. Simpson
Keyword(s):  
General Framework ◽  
Filippov Systems ◽  
Boundary Equilibrium

scholarly journals NONHYPERBOLIC BOUNDARY EQUILIBRIUM BIFURCATIONS IN PLANAR FILIPPOV SYSTEMS: A CASE STUDY APPROACH

2008 ◽  
Vol 18 (05) ◽  
pp. 1377-1392 ◽  
Author(s):  
MARIO DI BERNARDO ◽  
DANIEL J. PAGANO ◽  
ENRIQUE PONCE
Keyword(s):  
Equilibrium Point ◽  
Nonlinear Phenomena ◽  
Discontinuous Systems ◽  
Case Study Approach ◽  
Filippov Systems ◽  
Study Approach ◽  
Codimension One ◽  
Boundary Equilibrium ◽  
Two Parameter

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a nonhyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding biparametric bifurcation sets is developed.

scholarly journals Bifurcations of Finite-Time Stable Limit Cycles from Focus Boundary Equilibria in Impacting Systems, Filippov Systems, and Sweeping Processes

2018 ◽  
Vol 28 (10) ◽  
pp. 1850126 ◽  
Author(s):  
Oleg Makarenkov ◽  
Lakmi Niwanthi Wadippuli Achchige
Keyword(s):  
Limit Cycles ◽  
Finite Time ◽  
Stable Limit Cycle ◽  
Piecewise Smooth ◽  
Stable Limit ◽  
Bifurcation Of Limit Cycles ◽  
Filippov Systems ◽  
Boundary Equilibrium ◽  
Sweeping Processes ◽  
Linearized System

We establish a theorem on bifurcation of limit cycles from a focus boundary equilibrium of an impacting system, which is universally applicable to prove the bifurcation of limit cycles from focus boundary equilibria in other types of piecewise-smooth systems, such as Filippov systems and sweeping processes. Specifically, we assume that one of the subsystems of the piecewise-smooth system under consideration admits a focus equilibrium that lie on the switching manifold at the bifurcation value of the parameter. In each of the three cases, we derive a linearized system which is capable of concluding the occurrence of a finite-time stable limit cycle from the above-mentioned focus equilibrium when the parameter crosses the bifurcation value. Examples illustrate how conditions of our theorems lead to closed-form formulas for the coefficients of the linearized system.

scholarly journals Two Degenerate Boundary Equilibrium Bifurcations in Planar Filippov Systems

2011 ◽  
Vol 10 (4) ◽  
pp. 1525-1553 ◽  
Author(s):  
Fabio Dercole ◽  
Fabio Della Rossa ◽  
Alessandro Colombo ◽  
Yuri A. Kuznetsov
Keyword(s):  
Filippov Systems ◽  
Boundary Equilibrium

Phonologically conditioned allomorphy in the morphology of Surmiran (Rumantsch)

2008 ◽  
Vol 1 (2) ◽  
pp. 109-134 ◽  
Author(s):  
Stephen R. Anderson
Keyword(s):  
Optimality Theory ◽  
General Framework ◽  
Great Majority ◽  
Historical Change ◽  
Romance Languages ◽  
Morphological Properties ◽  
Entire System ◽  
Verbal System ◽  
Extended Sense ◽  
Phonological Rule

Alternations between allomorphs that are not directly related by phonological rule, but whose selection is governed by phonological properties of the environment, have attracted the sporadic attention of phonologists and morphologists. Such phenomena are commonly limited to rather small corners of a language's structure, however, and as a result have not been a major theoretical focus. This paper examines a set of alternations in Surmiran, a Swiss Rumantsch language, that have this character and that pervade the entire system of the language. It is shown that the alternations in question, best attested in the verbal system, are not conditioned by any coherent set of morphological properties (either straightforwardly or in the extended sense of ‘morphomes’ explored in other Romance languages by Maiden). These alternations are, however, straightforwardly aligned with the location of stress in words, and an analysis is proposed within the general framework of Optimality Theory to express this. The resulting system of phonologically conditioned allomorphy turns out to include the great majority of patterning which one might be tempted to treat as productive phonology, but which has been rendered opaque (and subsequently morphologized) as a result of the working of historical change.

More's usage of Latin verbal predicates: the particular case of fio

Moreana ◽  
2019 ◽  
Vol 56 (Number 211) (1) ◽  
pp. 97-120
Author(s):  
Concepción Cabrillana
Keyword(s):  
General Framework ◽  
Medieval Latin ◽  
Lexical Semantic ◽  
Syntactic Features ◽  
Comparative Review ◽  
Poetic Text

This article addresses Thomas More's use of an especially complex Latin predicate, fio, as a means of examining the degree of classicism in this aspect of his writing. To this end, the main lexical-semantic and syntactic features of the verb in Classical Latin are presented, and a comparative review is made of More's use of the predicate—and also its use in texts contemporaneous to More, as well as in Late and Medieval Latin—in both prose and poetry. The analysis shows that he works within a general framework of classicism, although he introduces some of his own idiosyncrasies, these essentially relating to the meaning of the verb that he employs in a preferential way and to the variety of verbal forms that occur in his poetic text.

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