]>
2016
16
4
103
Partially equi-integral \(\phi_0\)-stability of nonlinear differential systems
Partially equi-integral \(\phi_0\)-stability of nonlinear differential systems
en
en
This paper introduces the notions of partially equi-integral stability and partially equi-integral
\(\phi_0\)-stability for two differential systems, and establishes some criteria on stability relative to the \(x\)-component by using the cone-valued Lyapunov functions and the comparison technique. An example
is also given to illustrate our main results.
472
480
Junyan
Bao
Xiaojing
Liu
Peiguang
Wang
Differential systems
partially integral stability
partially integral \(\phi_0\)-stability
cone-valued Lyapunov functions
comparison technique.
Article.1.pdf
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[1]
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S. G. Hristova , Integral stability in terms of two measures for impulsive differential equations with ''supremum'' , Comm. Appl. Nonlinear Anal., 16 (2009), 37-49
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S. G. Hristova , Integral stability in terms of two measures for impulsive functional differential equations , Math. Comput. Modelling, 21 (2010), 100-108
##[5]
S. G. Hristova, I. K. Russinov, \(\phi_0\)-Integral stability in terms of two measures for differential equations, Math. Balkanica, 23 (2009), 133-144
##[6]
A. O. Ignatyve , On the Partial equiasymptotic stability in functional differential equations , J. Math. Anal. Appl., 268 (2002), 615-628
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V. Lakshmikantham, S. Leela , Differential and Integral Inequalities, Vol. I, Academic press, New York (1969)
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A. A. Soliman , On stability for impulsive perturbed systems via cone-valued Lyapunov function method, Appl. Math. Comput., 157 (2004), 269-279
##[9]
A. A. Soliman, M. H. Abd Alla, Integral stability criteria of nonlinear differential systems, Math. Comput. Modelling, 48 (2008), 258-267
]
Global attractivity of a two-species competitive system with nonlinear inter-inhibition terms
Global attractivity of a two-species competitive system with nonlinear inter-inhibition terms
en
en
Sufficient conditions are obtained for the global attractivity of the positive equilibrium and boundary equilibria of the following two-species competitive system with nonlinear inter-inhibition terms
\[\frac{dy_1(t)}{dt}=y_1(t)\left[r_1-a_1y_1-\frac{b_1y_2}{1+y_2}\right],\]
\[\frac{dy_2(t)}{dt}=y_2(t)\left[r_2-a_2y_2-\frac{b_2y_1}{1+y_1}\right],\]
where \(r_i, a_i, b_i, i = 1, 2\) are all positive constants. Our result shows that conditions which ensure the
permanence of the system are almost enough to ensure the global stability of the system. The results
not only improve but also complement the main results of Wang et al. [Q. L. Wang, Z. J. Liu, Z. X.
Li, R. A. Cheke, Int. J. Biomath., 7 (2014), 18 pages].
481
494
Baoguo
Chen
Competition
nonlinear inter-inhibition terms
global attractivity.
Article.2.pdf
[
[1]
F. D. Chen , On a nonlinear nonautonomous predator-prey model with diffusion and distributed delay, J. Comput. Appl. Math., 180 (2005), 33-49
##[2]
F. D. Chen , Average conditions for permanence and extinction in nonautonomous Gilpin-Ayala competition model, Nonlinear Anal. Real World Appl., 7 (2006), 895-915
##[3]
F. D. Chen, Some new results on the permanence and extinction of nonautonomous Gilpin-Ayala type competition model with delays, Nonlinear Anal. Real World Appl., 7 (2006), 1205-1222
##[4]
L. J. Chen, J. T. Sun, F. D. Chen, L. Zhao , Extinction in a Lotka-Volterra competitive system with impulse and the effect of toxic substances , Appl. Math. Model. , 40 (2016), 2015-2024
##[5]
F. D. Chen, H. N. Wang, Dynamic behaviors of a Lotka-Volterra competitive system with infinite delays and single feedback control, J. Nonlinear Funct. Anal., 2016 (2016 ), 1-21
##[6]
F. D. Chen, H. N. Wang, Y. H. Lin, W. L. Chen , Global stability of a stage-structured predator-prey system , Appl. Math. Comput., 223 (2013), 45-53
##[7]
F. D. Chen, X. D. Xie, Z. Li , Partial survival and extinction of a delayed predator-prey model with stage structure, Appl. Math. Comput., 219 (2012), 4157-4162
##[8]
F. D. Chen, X. D. Xie, Z. S. Miao, L. Q. Pu , Extinction in two species nonautonomous nonlinear competitive system, Appl. Math. Comput., 274 (2016), 119-124
##[9]
F. D. Chen, X. D. Xie, H. N. Wang, Global stability in a competition model of plankton allelopathy with infinite delay, J. Syst. Sci. Complex., 28 (2015), 1070-1079
##[10]
F. D. Chen, M. S. You, Permanence for an integrodifferential model of mutualism , Appl. Math. Comput., 186 (2007), 30-34
##[11]
K. Gopalsamy , Stability and oscillations in delay differential equations of population dynamics, Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht (1992)
##[12]
M. X. He, Z. Li, F. D. Chen , Permanence, extinction and global attractivity of the periodic Gilpin-Ayala competition system with impulses , Nonlinear Anal. Real World Appl., 11 (2010), 1537-1551
##[13]
Z. Li, F. D. Chen , Extinction in periodic competitive stage-structured Lotka-Volterra model with the effects of toxic substances , J. Comput. Appl. Math., 231 (2009), 143-153
##[14]
Z. Li, F. D. Chen, M. X. He, Asymptotic behavior of the reaction-diffusion model of plankton allelopathy with nonlocal delays , Nonlinear Anal. Real World Appl., 12 (2011), 1748-1758
##[15]
Z. Li, F. D. Chen, M. X. He, Global stability of a delay differential equations model of plankton allelopathy, Appl. Math. Comput., 218 (2012), 7155-7163
##[16]
Z. Li, M. Han, F. D. Chen , Global stability of a stage-structured predator-prey model with modified Leslie-Gower and Holling-type II schemes, Int. J. Biomath., 5 (2012), 1-13
##[17]
Y. H. Lin, X. D. Xie, F. D. Chen, T. T. Li , Convergences of a stage-structured predator-prey model with modified Leslie-Gower and Holling-type II schemes , Adv. Difference Equ., 2016 (2016 ), 1-19
##[18]
L. Q. Pu, X. D. Xie, F. D. Chen, Z. S. Miao , Extinction in two-species nonlinear discrete competitive system , Discrete Dyn. Nat. Soc., 2016 (2016 ), 1-10
##[19]
W. J. Qin, Z. J. Liu, Y. P. Chen, Permanence and global stability of positive periodic solutions of a discrete competitive system, Discrete Dyn. Nat. Soc., 2009 (2009 ), 1-13
##[20]
C. L. Shi, Z. Li, F. D. Chen , Extinction in a nonautonomous Lotka-Volterra competitive system with infinite delay and feedback controls, Nonlinear Anal. Real World Appl., 13 (2012), 2214-2226
##[21]
Q. L. Wang, Z. J. Liu , Uniformly asymptotic stability of positive almost periodic solutions for a discrete competitive system, J. Appl. Math., 2013 (2013 ), 1-9
##[22]
Q. L. Wang, Z. J. Liu, Z. X. Li, Positive almost periodic solutions for a discrete competitive system subject to feedback controls, J. Appl. Math., 2013 (2013 ), 1-14
##[23]
Q. L. Wang, Z. J. Liu, Z. X. Li, R. A. Cheke , Existence and global asymptotic stability of positive almost periodic solutions of a two-species competitive system, Int. J. Biomath., 7 (2014), 1-18
##[24]
X. D. Xie, F. D. Chen, Y. L. Xue , Note on the stability property of a cooperative system incorporating harvesting, Discrete Dyn. Nat. Soc., 2014 (2014 ), 1-5
##[25]
X. D. Xie, F. D. Chen, K. Yang, Y. L. Xue , Global attractivity of an integrodifferential model of mutualism, Abstr. Appl. Anal., 2014 (2014 ), 1-6
##[26]
K. Yang, X. D. Xie, F. D. Chen, Global stability of a discrete mutualism model, Abstr. Appl. Anal., 2014 (2014 ), 1-7
##[27]
S. B. Yu , Global asymptotic stability of a predator-prey model with modified Leslie-Gower and Holling- type II schemes, Discrete Dyn. Nat. Soc., 2012 (2012 ), 1-8
##[28]
S. B. Yu, Permanence for a discrete competitive system with feedback controls , Commun. Math. Biol. Neurosci., 2015 (2015 ), 1-11
##[29]
Q. Yue , Dynamics of a modified LeslieGower predatorprey model with Holling-type II schemes and a prey refuge , SpringerPlus, 5 (2016), 1-12
]
Dynamic behaviors of a commensal symbiosis model with ratio-dependent functional response and one party can not survive independently
Dynamic behaviors of a commensal symbiosis model with ratio-dependent functional response and one party can not survive independently
en
en
We propose a two-species commensal symbiosis model with ratio-dependent functional response
\[\frac{dx}{dt}=x\left(-a_1-b_1x+\frac{c_1y}{x+y}\right),\]
\[\frac{dy}{dt}=y\left(a_2-b_2y\right),\]
For autonomous case, we show that the unique positive equilibrium is globally stable if \(a_1 < c_1\) holds,
and the boundary equilibrium \((0, \frac{a_2}{b_2})\) is globally stable if \(a_1 > c_1\) holds. For nonautonomous case,
some sufficient conditions which ensure the permanence and global attractivity of the system are
obtained. Numeric simulations are carried out to show the feasibility of the main results.
495
506
Runxin
Wu
Lin
Li
Commensal symbiosis model
stability.
Article.3.pdf
[
[1]
F. D. Chen, Permanence for the discrete mutualism model with time delays, Math. Comput. Modelling, 47 (2008), 431-435
##[2]
L. J. Chen, L. J. Chen, Z. Li , Permanence of a delayed discrete mutualism model with feedback controls, Math. Comput. Modelling, 50 (2009), 1083-1089
##[3]
F. D. Chen, Z. Li, Y. J. Huang , Note on the permanence of a competitive system with infinite delay and feedback controls, Nonlinear Anal. Real World Appl., 8 (2007), 680-687
##[4]
F. D. Chen, C. T. Lin, L. Y. Yang, On a discrete obligate Lotka-Volterra model with one party can not surivive independently, Journal of Shenyang University (Natural Science), 4 (2015), 336-338
##[5]
F. D. Chen, L. Q. Pu, L. Y. Yang , Positive periodic solution of a discrete obligate Lotka-Volterra model , Commun. Math. Biol. Neurosci., 2015 (2015 ), 1-9
##[6]
F. D. Chen, J. L. Shi , On a delayed nonautonomous ratio-dependent predator-prey model with Holling type functional response and diffusion, Appl. Math. Comput., 192 (2007), 358-369
##[7]
L. S. Chen, X. Y. Song, Z. Y. Lu, Mathematical models and methods in ecology , (Chinese) Shichuan Science and Technology Press, Chengdu (2002), -
##[8]
L. J. Chen, X. D. Xie , Permanence of an N-species cooperation system with continuous time delays and feedback controls , Nonlinear Anal. Real World Appl., 12 (2011), 34-38
##[9]
F. D. Chen, X. D. Xie , Study on the dynamic behaviors of cooperation population modeling , (Chinese) Science Press, Beijing (2014)
##[10]
L. J. Chen, X. D. Xie, L. J. Chen , Feedback control variables have no in uence on the permanence of a discrete N-species cooperation system , Discrete Dyn. Nat. Soc., 2009 (2009 ), 1-10
##[11]
F. D. Chen, X. D. Xie, X. F. Chen, Dynamic behaviors of a stage-structured cooperation model, Commun. Math. Biol. Neurosci., 2015 (2015 ), 1-19
##[12]
F. D. Chen, J. H. Yang, L. J. Chen, X. D. Xie, On a mutualism model with feedback controls, Appl. Math. Comput., 214 (2009), 581-587
##[13]
M. Fan, K. Wang, Periodicity in a delayed ratio-dependent predator-prey system, J. Math. Anal. Appl., 262 (2001), 179-190
##[14]
Y. K. Li, T. W. Zhang , Permanence of a discrete n-species cooperation system with time-varying delays and feedback controls, Math. Comput. Modelling, 53 (2011), 1320-1330
##[15]
Z. J. Liu, J. H. Wu, R. H. Tan, Y. P. Chen , Modeling and analysis of a periodic delayed two-species model of facultative mutualism , Appl. Math. Comput., 217 (2010), 893-903
##[16]
Z. S. Miao, X. D. Xie, L. Q. Pu , Dynamic behaviors of a periodic Lotka-Volterra commensal symbiosis model with impulsive, Commun. Math. Biol. Neurosci., 2015 (2015 ), 1-15
##[17]
R. X. Wu, L. Lin, X. Y. Zhou, A commensal symbiosis model with Holling type functional response, J. Math. Computer Sci., 16 (2016), 364-371
##[18]
D. M. Xiao, W. X. Li, M. A. Han , Dynamics in a ratio-dependent predator-prey model with predator harvesting, J. Math. Anal. Appl., 325 (2006), 14-29
##[19]
X. D. Xie, F. D. Chen, Y. L. Xue, Note on the stability property of a cooperative system incorporating harvesting, Discrete Dyn. Nat. Soc., 2014 (2014 ), 1-5
##[20]
X. D. Xie, F. D. Chen, K. Yang, Y. L. Xue, Global attractivity of an integrodifferential model of mutualism, Abstr. Appl. Anal., 2014 (2014 ), 1-6
##[21]
X. D. Xie, Z. S. Miao, Y. L. Xue, Positive periodic solution of a discrete Lotka-Volterra commensal symbiosis model, Commun. Math. Biol. Neurosci., 2015 (2015 ), 1-10
##[22]
X. D. Xie, Y. L. Xue, J. H. Chen, T. T. Li, Permanence and global attractivity of a nonautonomous modified Leslie-Gower predator-prey model with Holling-type II schemes and a prey refuge, Adv. Difference Equ., 2016 (2016 ), 1-11
##[23]
Y. L. Xue, F. D. Chen, X. D. Xie, R. Y. Han , Dynamic behaviors of a discrete commensalism system, Ann. Appl. Math., 31 (2015), 452-461
##[24]
Y. L. Xue, X. D. Xie, F. D. Chen, R. Y. Han , Almost periodic solution of a discrete commensalism system , Discrete Dyn. Nat. Soc., 2015 (2015 ), 1-11
##[25]
L. Y. Yang, R. Y. Han, Y. L. Xue, F. D. Chen , On a Nonautonomous Obligate Lotka-Volterra Model, J. Sanming Univ., 6 (2014), 15-18
##[26]
W. S. Yang, X. P. Li, Permanence of a discrete nonlinear N-species cooperation system with time delays and feedback controls, Appl. Math. Comput., 218 (2011), 3581-3586
##[27]
K. Yang, Z. S. Miao, F. D. Chen, X. D. Xie, Influence of single feedback control variable on an autonomous Holling-II type cooperative system,, J. Math. Anal. Appl., 435 (2016), 874-888
##[28]
K. Yang, X. D. Xie, F. D. Chen , Global stability of a discrete mutualism model, Abstr. Appl. Anal., 2014 (2014 ), 1-7
##[29]
Z. F. Zhu, Y. A. Li, F. Xu, Mathematical analysis on commensalism Lotka-Volterra model of populations, Chongqing Institute of Technology (Natural Science), 21 (2007), 59-62
]
Directional differentiability of interval-valued functions
Directional differentiability of interval-valued functions
en
en
In this paper, by using the generalized Hukuhara difference (gH-difference) of interval numbers,
we introduce and study the directional differentiability problem of interval-valued function. Firstly,
we put forward the concept of directional differentiability of interval-valued function, discuss the
characterizations of directional differentiability of interval-valued function, and propose the sufficient
condition of the directional differentiability of interval-valued function. Secondly, we discuss the relations among the directional derivative, derivative and partial derivative of interval-valued function,
and prove that the derivative and partial derivative are both special directional derivatives.
507
515
Yu-e
Bao
Bo
Zao
Eer-dun
Bai
Interval numbers
interval-valued function
Hausdorff metric
generalized H-difference
directional derivative.
Article.4.pdf
[
[1]
B. Bede, L. Stefanini , Generalized differentiability of fuzzy-valued functions, Fuzzy Sets and Systems, 230 (2013), 119-141
##[2]
Y. Chalco-Cano, H. Roman-Flores, M. D. Jimenez-Gamero, Generalized derivative and \(\pi\)-derivative for set-valued functions, Inform. Sci., 181 (2011), 2177-2188
##[3]
Y. Chalco-Cano, A. Rufián-Lizan, H. Román-Flores, M. D. Jiménez-Gamero, Calculus for interval- valued functions using generalized Hukuhara derivative and applications, Fuzzy Sets and Systems, 219 (2013), 49-67
##[4]
V. Lupulescu, Fractional calculus for interval-valued functions , Fuzzy Sets and Systems, 265 (2015), 63-85
##[5]
R. E. Moore, Interval Analysis,Prentice-Hall , Englewood Cliffs, New Jersey (1966)
##[6]
R. Osuna-Gómez, Y. Chalco-Cano, B. Hernández -Jiménez, G. Ruiz-Garzn, Optimality conditions for generalized differentiable interval-valued functions, Inform Sci., 321 (2015), 136-146
##[7]
L. Stefanini, B. Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Anal., 71 (2009), 1311-1328
##[8]
H.-C. Wu, The KarushKuhnTucker optimality conditions in multiobjective programming problems with interval-valued objective functions , European J. Oper. Res., 196 (2009), 49-60
]
Fixed and common fixed point theorems in partially ordered quasi-metric spaces
Fixed and common fixed point theorems in partially ordered quasi-metric spaces
en
en
In this paper, we prove some new fixed and common fixed point results in the framework of
partially ordered quasi-metric spaces under linear and nonlinear contractions. Also we obtain some
fixed point results in the framework of G-metric spaces.
516
528
Wasfi
Shatanawi
Mohd Salmi MD
Noorani
Habes
Alsamir
Anwar
Bataihah
Quasi metric
common fixed point theorem
nonlinear contraction
altering distance function
G-metric spaces.
Article.5.pdf
[
[1]
R. P. Agarwal, M. A. El-Gebeily, D. O'Regan , Generalized contractions in partially ordered metric spaces , Appl. Anal., 87 (2008), 109-116
##[2]
R. P. Agarwal. E. Karapınar, A. F. Roldán-López-de-Hierro , Last remarks on G-metric spaces and related fixed point theorems , Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 110 (2016), 433-456
##[3]
I. Altun, H. Simsek, Some fixed point theorems on orderd metric spaces and applications, Fixed Point Theory Appl., 2010 (2010), 1-17
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S. Banach , Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
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M. Jleli, B. Samet, Remarks on G-metric spaces and fixed point theorems, Fixed Point Theory Appl., 2012 (2012 ), 1-7
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N. V. Luong, N. X. Thuan , Coupled fixed point theorems in partially ordered G-metric spaces , Math. Comput. Modelling, 55 (2012), 1601-1609
##[8]
Z. Mustafa , Common fixed points of weakly compatible mappings in G-metric spaces, Appl. Math. Sci. (Ruse), 6 (2012), 4589-4600
##[9]
Z. Mustafa , Some new common fixed point theorems under strict contractive conditions in G-metric spaces, J. Appl. Math., 2012 (2012), 1-21
##[10]
Z. Mustafa, M. Khandaqji, W. Shatanawi, Fixed point results on complete G-metric spaces, Studia Sci. Math. Hungar., 48 (2011), 304-319
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Z. Mustafa, H. Obiedat , A fixed point theorem of Reich in G-metric spaces , Cubo, 12 (2010), 83-93
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Z. Mustafa, H. Obiedat, F. Awawdeh, Some fixed point theorem for mapping on complete G-metric spaces , Fixed Point Theory Appl., 2008 (2008 ), 1-12
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Z. Mustafa, W. Shatanawi, M. Bataineh , Existence of fixed point results in G-metric spaces, Int. J. Math. Math. Sci., 2009 (2009 ), 1-10
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Z. Mustafa, B. Sims , Fixed point theorems for contractive mappings in complete G-metric spaces , Fixed Point Theory Appl., 2009 (2009 ), 1-10
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B. Samet, C. Vetro, F. Vetro, Remarks on G-metric spaces, Int. J. Anal., 2013 (2013 ), 1-6
##[17]
W. Shatanawi, M. Postolache , Some fixed-point results for a G-weak contraction in G-metric spaces, Abstr. Appl. Anal., 2012 (2012 ), 1-19
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W. Shatanawi, M. Postolache, Common fixed point results for mappings under nonlinear contraction of cyclic form in ordered metric spaces, Fixed Point Theory Appl., 2013 (2013 ), 1-13
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W. A. Wilson , On quasi-metric spaces , Amer. J. Math., 53 (1931), 675-684
]
Analysis of electro-visco-elastic contact problem with friction
Analysis of electro-visco-elastic contact problem with friction
en
en
A quasistatic frictional contact problem is studied. The material behavior is modeled with a
nonlinear electro-visco-elastic constitutive law, allowing piezoelectric effects. The body may come
into contact with a rigid obstacle. Contact is described with the Signorini condition, a version
of Coulomb's law of dry friction, and a regularized electrical conductivity condition. We derive a
variational formulation of the problem, then, under a smallness assumption on the coefficient of
friction, we prove an existence and uniqueness result of a weak solution for the model. The proof
is based on arguments of elliptic variational inequalities and fixed points of operators.
529
540
A.
Bachmar
T.
Serrar
Piezoelectric
frictional contact
electro-visco-elastic
fixed point
quasistatic process
Coulomb's friction law
variational inequality.
Article.6.pdf
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##[3]
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##[12]
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]
C-erasure reconstruction error of \({GC}\)-frame of subspaces
C-erasure reconstruction error of \({GC}\)-frame of subspaces
en
en
In [M. H. Faroughi, R. Ahmadi, Math. Nachr., 284 (2010), 681-693], we generalized the concept
of fusion frames, namely, c-fusion integral, which is a continuous version of the fusion frames and
in [M. H. Faroughi, A. Rahimi, R. Ahmadi, Methods Funct. Anal. Topology, 16 (2010), 112-119]
we extended it for generalized frames. In this article we give some important properties about it
namely erasures of subspaces, the bound of gc-erasure reconstruction error for Parseval gc-frame of
subspaces.
541
553
Reza
Ahmadi
Hosein
Emamalipor
Operator theory
frame
Hilbert space
fusion frame
generalized frame.
Article.7.pdf
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P. G. Casazza, J. Kovačević, Equal-norm tight frames with erasures , Adv. Comput. Math., 18 (2003), 387-430
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P. G. Casazza, G. Kutyniok, S. D. Li , Fusion frames and distributed processing , Appl. Comput. Harmon. Anal., 25 (2008), 114-132
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Controllability properties of bilinear systems in dimension 2
Controllability properties of bilinear systems in dimension 2
en
en
This paper discusses the controllability of bilinear control systems by considering the spectrum
of the system and controllability of the projection onto the projective space. Necessary and sufficient
conditions are presented for two dimensional systems with bounded and unbounded control range.
554
575
Victor
Ayala
Efrain
Cruz
Wolfgang
Kliemann
Leonardo R.
Laura-guarachi
Bilinear control systems
controllability
spectrum
projected linear system.
Article.8.pdf
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