2020
11
1
0
100
Kato's chaos and Pchaos of a coupled lattice system given by Garcia Guirao and Lampart which is related with BelusovZhabotinskii reaction
2
2
In this article, we further consider the above system. In particular, we give a sufficient condition under which the above system is Kato chaotic for $eta=0$ and a necessary condition for the above system to be Kato chaotic for $eta=0$. Moreover, it is deduced that for $eta=0$, if $Theta$ is Pchaotic then so is this system, where a continuous map $Theta$ from a compact metric space $Z$ to itself is said to be Pchaotic if it has the pseudoorbittracing property and the closure of the set of all periodic points for $Theta$ is the space $Z$. Also, an example and three open problems are presented.
1

1
9


Risong
Li
Guangdong Ocean University
Guangdong Ocean University
P. R. China
gdoulrs@163.com
Coupled map lattice
Kato's chaos
Pchaos
LiYorke's chaos
Tent map
[T. Y. Li and J. A. Yorke, Period three implies chaos, Am. Math. Mon. 82 (10) (1975) 985992.##L. S. Block and W. A. Coppel, Dynamics in One Dimension, Springer Monographs in Mathematics, Springer, Berlin, 1992.##R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Benjamin/ Cumings, Menlo Park, CA, 1986.##J. R. Chazottes and B. Fern Andez, Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems, Lecture Notes in Physics (Berlin Heidelberg New York Springer), Vol. 671, 2005.##J. L. García Guirao and M. Lampart, Positive entropy of a coupled lattice system related with BelusovZhabotinskii reaction, J. Math. Chem. 48 (2010) 6671.##K. Kaneko, Globally coupled chaos violates law of large numbers, Phys. Rev. Lett. 65 (1990) 13911394.##J. L. García Guirao and M. Lampart, Chaos of a coupled lattice system related with BelusovZhabotinskii reaction, J. Math. Chem. 48 (2010) 159164.##M. Kohmoto and Y. Oono, Discrete model of chemical turbulence, Phys. Rev. Lett. 55 (1985) 29272931.##J. L. Hudson, M. Hart and D. Marinko, An experimental study of multiplex peak periodic and nonperiodic oscilations in the BelusovZhabotinskii reaction, J. Chem. Phys. 71 (1979) 16011606.##K. Hirakawa, Y. Oono and H. Yamakazi, Experimental study on chemical turbulence II, J. Phys. Soc. Jap. 46 (1979) 721728.##J. L. Hudson, K. R. Graziani, R. A. Schmitz, Experimental evidence of chaotic states in the BelusovZhabotinskii reaction, J. Chem. Phys. 67 (1977) 30403044.##D. Ruelle and F. Takens, On the natural of turbulence, Comm. Math. Phys. 20 (1971) 16792.##H. Kato, Everywhere chaotic homeomorphisms on manifields and kdimensional Menger manifolds, Topol. Appl. 72 (1996) 117.##R. Gu, Kato’s chaos in setvalued discrete systems, Chaos, Solitons & Fractals 31 (2007) 765771.##G. L. Forti, Various notions of chaos for discrete dynamical systems, A brief survey, Aequationes Math. 70 (2005) 113.##X. Wu and P. Zhu, On sensitive dependence of continuous interval mappings (In Chinese), J. Systems Sci. Math. Sci. 32 (2012) 215225.##T. Arai and N. Chinen, Pchaos implies distributional chaos and chaos in the sense of Devaney with positive topological entropy, Topol. Appl. 154 (2007) 12541262. ##X. Wu, P. Oprocha and G. Chen, On various definitions of shadowing with average error in tracing, Nonlinearity 29 (2016) 19421972.##F. Balibrea, On problems of topological dynamics in nonautonomous discrete systems, Appl. Math. Nonlinear Sci. 1 (2) (2016) 391404.##]
On Topological Indices Of the nStar Graph
2
2
The nstar graph Sn is defined on the set of all n sequenses (u1,u2,...,un), ui ∈ {1, 2, ..., n}, ui ne uj and i ne j, where edges are of the form (u1,u2,...,un) ∼ (ui,u2,...,un), for some i ne 1. In this paper we will show that Sn is a vertex and edge transitive graph and discuss some topological properties of Sn.
1

11
16


Negur
Karamzadeh
Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
Department of Mathematics, Faculty of Mathematical
I R Iran
n_shahni@sbu.ac.ir


Mohammad
Darafsheh
University of Tehran
University of Tehran
I R Iran
darafsheh@ut.ac.ir
Star graph
Vertex transitive graph
edge transitive graph
Wiener index
[S. B. Akers, D. Harel and B. Krishnamurthy, The star graph: An attractive alternative to the ncube, Proc. International Conference on Parallel Processing, St. Charles, Illinois, 1987, pp. 393400.##W. K. Chiang and R. J. Chen, The (n, k)star graph: A generalized star graph, Info. Proc. Lett. 56 (1995) 259264.##M. R. Darafsheh, Computation of topological indices of some graphs, Acta Appl. Math. 110 (2010) 12251235.##I. Gutman, S. Klavžar and B. Mohr (eds), Fifty years of the Wiener index, MATCH Commun. Math. Comput. Chem. 35 (1997) 1259.##I. Gutman, Y. N. Yeh, S. L. Lee and J. C. Chen, Wiener numbers of dendrimers, MATCH Commun. Math. Comput. Chem. 30 (1994)103115.##K. Qiu and S. G. Akl, On some properties of the star graph, VLSI Design, 2 (4) (1995) 389396.##H. Shabani and A. R. Ashrafi, SymmetryModerated Wiener index, MATCH Commun. Math. Comput Chem. 76 (2016) 318.##H. Wiener, Structural determination of paraffin boiling points, J. Am. Chm. Soc. 69 (1947) 1720.##]