American Institute of Mathematical Sciences

• Previous Article
Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption
• DCDS Home
• This Issue
• Next Article
Dynamics for a non-autonomous reaction diffusion model with the fractional diffusion
December  2017, 37(12): 6069-6098. doi: 10.3934/dcds.2017261

Impulsive motion on synchronized spatial temporal grids

 1 Worcester Polytechnic Institute, 100 Worcester Road, Worcester, MA 01609, USA 2 Accademia Nazionale Delle Scienze Detta Dei XL, Via L.Spallanzani 7, 00161 Roma, Italy

Received  August 2016 Revised  July 2017 Published  August 2017

We introduce a family of kinetic vector fields on countable space-time grids and study related impulsive second order initial value Cauchy problems. We then construct special examples for which orbits and attractors display unusual analytic and geometric properties.

Citation: Umberto Mosco. Impulsive motion on synchronized spatial temporal grids. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6069-6098. doi: 10.3934/dcds.2017261
References:

show all references

References:
$\Gamma^{\beta, n}$ for different $\beta$
Ring-like $\Gamma^{\beta, n}$
 [1] Michael L. Frankel, Victor Roytburd. Fractal dimension of attractors for a Stefan problem. Conference Publications, 2003, 2003 (Special) : 281-287. doi: 10.3934/proc.2003.2003.281 [2] Sergey Dashkovskiy, Oleksiy Kapustyan, Iryna Romaniuk. Global attractors of impulsive parabolic inclusions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1875-1886. doi: 10.3934/dcdsb.2017111 [3] Andrey Zvyagin. Attractors for model of polymer solutions motion. Discrete & Continuous Dynamical Systems - A, 2018, 38 (12) : 6305-6325. doi: 10.3934/dcds.2018269 [4] Yong Ren, Wensheng Yin, Dongjin Zhu. Exponential stability of SDEs driven by $G$-Brownian motion with delayed impulsive effects: average impulsive interval approach. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3347-3360. doi: 10.3934/dcdsb.2018248 [5] Michael Barnsley, James Keesling, Mrinal Kanti Roychowdhury. Special issue on fractal geometry, dynamical systems, and their applications. Discrete & Continuous Dynamical Systems - S, 2019, 12 (8) : ⅰ-ⅰ. doi: 10.3934/dcdss.201908i [6] Michael Basin, Pablo Rodriguez-Ramirez. An optimal impulsive control regulator for linear systems. Numerical Algebra, Control & Optimization, 2011, 1 (2) : 275-282. doi: 10.3934/naco.2011.1.275 [7] George Ballinger, Xinzhi Liu. Boundedness criteria in terms of two measures for impulsive systems. Conference Publications, 1998, 1998 (Special) : 79-88. doi: 10.3934/proc.1998.1998.79 [8] Alberto Bressan. Impulsive control of Lagrangian systems and locomotion in fluids. Discrete & Continuous Dynamical Systems - A, 2008, 20 (1) : 1-35. doi: 10.3934/dcds.2008.20.1 [9] John R. Graef, János Karsai. Oscillation and nonoscillation in nonlinear impulsive systems with increasing energy. Conference Publications, 2001, 2001 (Special) : 166-173. doi: 10.3934/proc.2001.2001.166 [10] Xueyan Yang, Xiaodi Li, Qiang Xi, Peiyong Duan. Review of stability and stabilization for impulsive delayed systems. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1495-1515. doi: 10.3934/mbe.2018069 [11] Yong Ren, Xuejuan Jia, Lanying Hu. Exponential stability of solutions to impulsive stochastic differential equations driven by $G$-Brownian motion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2157-2169. doi: 10.3934/dcdsb.2015.20.2157 [12] María Anguiano, Alain Haraux. The $\varepsilon$-entropy of some infinite dimensional compact ellipsoids and fractal dimension of attractors. Evolution Equations & Control Theory, 2017, 6 (3) : 345-356. doi: 10.3934/eect.2017018 [13] Francesco Fassò, Andrea Giacobbe, Nicola Sansonetto. On the number of weakly Noetherian constants of motion of nonholonomic systems. Journal of Geometric Mechanics, 2009, 1 (4) : 389-416. doi: 10.3934/jgm.2009.1.389 [14] Matthias Morzfeld, Daniel T. Kawano, Fai Ma. Characterization of damped linear dynamical systems in free motion. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 49-62. doi: 10.3934/naco.2013.3.49 [15] Tai-Ping Liu, Shih-Hsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete & Continuous Dynamical Systems - A, 2000, 6 (1) : 143-145. doi: 10.3934/dcds.2000.6.143 [16] Honglei Xu, Kok Lay Teo, Weihua Gui. Necessary and sufficient conditions for stability of impulsive switched linear systems. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1185-1195. doi: 10.3934/dcdsb.2011.16.1185 [17] Xiaowei Tang, Xilin Fu. New comparison principle with Razumikhin condition for impulsive infinite delay differential systems. Conference Publications, 2009, 2009 (Special) : 739-743. doi: 10.3934/proc.2009.2009.739 [18] Pavel Drábek, Martina Langerová. Impulsive control of conservative periodic equations and systems: Variational approach. Discrete & Continuous Dynamical Systems - A, 2018, 38 (8) : 3789-3802. doi: 10.3934/dcds.2018164 [19] Elena K. Kostousova. State estimation for linear impulsive differential systems through polyhedral techniques. Conference Publications, 2009, 2009 (Special) : 466-475. doi: 10.3934/proc.2009.2009.466 [20] Yejuan Wang, Chengkui Zhong, Shengfan Zhou. Pullback attractors of nonautonomous dynamical systems. Discrete & Continuous Dynamical Systems - A, 2006, 16 (3) : 587-614. doi: 10.3934/dcds.2006.16.587

2018 Impact Factor: 1.143