filippov type
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2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Rui Qu ◽  
Shaolong Li

The main purpose of this paper is to investigate the qualitative effects of external excitation and friction factor on the response of permanent magnet synchronous motor (PMSM) system. Three different modes of bursting oscillations are found. In particular, the introduction of friction function changes the governing equations from a smooth type to a nonsmooth (Filippov) type in which the special sliding motion is observed. The mechanism, attractor structure, vector field structure, and analytic bifurcation conditions of bursting oscillation and sliding motion are discussed in detail. The validity of theoretical results obtained is verified by numerical simulations and analysis.


2021 ◽  
Vol 66 (1) ◽  
pp. 17-27
Author(s):  
Aurelian Cernea

We study a Cauchy problem of a class of nonconvex second-order integro-differential inclusions and a boundary value problem associated to a semilinear evolution inclusion defined by nonlocal conditions in non-separable Banach spaces. The existence of mild solutions is established under Filippov type assumptions.


Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 12
Author(s):  
Reny George ◽  
Hemanth Kumar Pathak

The Hβ-Hausdorff–Pompeiu b-metric for β∈[0,1] is introduced as a new variant of the Hausdorff–Pompeiu b-metric H. Various types of multi-valued Hβ-contractions are introduced and fixed point theorems are proved for such contractions in a b-metric space. The multi-valued Nadler contraction, Czervik contraction, q-quasi contraction, Hardy Rogers contraction, weak quasi contraction and Ciric contraction existing in literature are all one or the other type of multi-valued Hβ-contraction but the converse is not necessarily true. Proper examples are given in support of our claim. As applications of our results, we have proved the existence of a unique multi-valued fractal of an iterated multifunction system defined on a b-metric space and an existence theorem of Filippov type for an integral inclusion problem by introducing a generalized norm on the space of selections of the multifunction.


2020 ◽  
Vol 30 (12) ◽  
pp. 2050168
Author(s):  
Hongfang Han ◽  
Qinsheng Bi

The main purpose of this paper is to explore the bursting oscillations as well as the mechanism of a parametric and external excitation Filippov type system (PEEFS), in which different types of bursting oscillations such as fold/nonsmooth fold (NSF)/fold/NSF, fold/NSF/fold and fold/fold bursting oscillations can be observed. By employing the overlap of the transformed phase portrait and the equilibrium branches of the generalized autonomous system, the mechanisms of the bursting oscillations are investigated. Our results show that the fold bifurcation and the boundary equilibrium bifurcation (BEB) can cause the transitions between the quiescent states and repetitive spiking states. The oscillating frequencies of the spiking states can be approximated theoretically by their occurring mechanisms, which agree well with the numerical simulations. Furthermore, some nonsmooth evolutions are investigated by employing differential inclusions theory, which reveals that the positional relationship between the points of the trajectory interacting with the nonsmooth boundary and the related sliding boundary of the nonsmooth system may affect the nonsmooth evolutions.


2020 ◽  
Vol 137 (6) ◽  
pp. 1089-1094
Author(s):  
M.A. Mohammadi ◽  
M. Manouchehrizadeh ◽  
R.S. Rawat
Keyword(s):  
X Ray ◽  

2020 ◽  
Vol 100 (3) ◽  
pp. 2973-2987
Author(s):  
Tiago Carvalho ◽  
Douglas Duarte Novaes ◽  
Luiz Fernando Gonçalves

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