scholarly journals Finite-Time Set Reachability of Probabilistic Boolean Multiplex Control Networks

2022 ◽  
Vol 12 (2) ◽  
pp. 883
Author(s):  
Yuxin Cui ◽  
Shu Li ◽  
Yunxiao Shan ◽  
Fengqiu Liu

This study focuses on the finite-time set reachability of probabilistic Boolean multiplex control networks (PBMCNs). Firstly, based on the state transfer graph (STG) reconstruction technique, the PBMCNs are extended to random logic dynamical systems. Then, a necessary and sufficient condition for the finite-time set reachability of PBMCNs is obtained. Finally, the obtained results are effectively illustrated by an example.

Author(s):  
Chen Zhaolin ◽  
Hong Huimin ◽  
Zhang Jifeng

AbstractThe state controllability for generalised dynamical systems with constrained control is discussed in this paper. The main results of the paper are the following:(1) a necessary and sufficient condition of the state controllability in the sense of control energy or amplitude constrained for generalised dynamical systems is obtained;(2) a control function u(t) is constructed such thata) u(t) satisfies constrained energy or amplitude condition,b) the state driven by u(t) moves from an arbitrary x(0−) = x0 to x(T(x0)) = 0,c) the trajectory driven by u(t) has no impulsive behaviour within (0, T(x0)].


Author(s):  
Thomas Sinclair

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.


1996 ◽  
Vol 33 (01) ◽  
pp. 211-216 ◽  
Author(s):  
G. Falin

We obtain a necessary and sufficient condition for the interaction between a service system and an external environment under which the stationary joint distribution of the set of busy channels and the state of the external environment is given by a product-form formula.


Author(s):  
Robert Laister ◽  
Mikołaj Sierżęga

Abstract We derive a blow-up dichotomy for positive solutions of fractional semilinear heat equations on the whole space. That is, within a certain class of convex source terms, we establish a necessary and sufficient condition on the source for all positive solutions to become unbounded in finite time. Moreover, we show that this condition is equivalent to blow-up of all positive solutions of a closely-related scalar ordinary differential equation.


2011 ◽  
Vol 20 (07) ◽  
pp. 1171-1182 ◽  
Author(s):  
P. S. NEGI

The necessary and sufficient condition for dynamical stability is worked out for the sequences of relativistic star models which correspond to the well-defined and causal values of adiabatic sound speed, [Formula: see text], at the center. On the basis of the conditions obtained in this study, we show that the mass–radius (M-R) relation corresponding to the MIT bag models of strange quark matter (SQM) and the models obtained by Dey et al. [Phys. Lett. B438 (1998) 123] does not provide the necessary and sufficient condition for dynamical stability for the equilibrium configurations. These findings will remain unaltered and can be extended to any other sequence of pure SQM. This study explicitly shows that though SQM may exist in the state of zero pressure and temperature, the models of pure strange quark "stars" cannot exist in the state of hydrostatic equilibrium. This study can affect the results which are claiming that various objects, like RX J1856.5-3754, SAX J1808.4-3658, 4U 1728-34 and PSR 0943+10, represent strange stars.


Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2139
Author(s):  
Jiale Sheng ◽  
Wei Jiang ◽  
Denghao Pang ◽  
Sen Wang

This paper is concerned with controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel. First, the solution of fractional dynamical systems with a Mittag–Leffler kernel is given by Laplace transform. In addition, one necessary and sufficient condition for controllability of linear fractional dynamical systems with Mittag–Leffler kernel is established. On this basis, we obtain one sufficient condition to guarantee controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel by fixed point theorem. Finally, an example is given to illustrate the applicability of our results.


2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Songlin Wo ◽  
Xiaoxin Han

The finite-time stability (FTS) problem of discrete-time linear singular systems (DTLSS) is considered in this paper. A necessary and sufficient condition for FTS is obtained, which can be expressed in terms of matrix inequalities. Then, another form of the necessary and sufficient condition for FTS is also given by using matrix-null space technology. In order to solve the stability problem expediently, a sufficient condition for FTS is given via linear matrix inequality (LMI) approach; this condition can be expressed in terms of LMIs. Finally, an illustrating example is also given to show the effectiveness of the proposed method.


2012 ◽  
Vol 13 (01) ◽  
pp. 1250008
Author(s):  
ARNO BERGER ◽  
STEVEN N. EVANS

A short proof utilizing dynamical systems techniques is given of a necessary and sufficient condition for the normalized occupation measure of a Lévy process in a metrizable compact group to be asymptotically uniform with probability one.


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