All Issues

Volume 42, 2022

Volume 41, 2021

Volume 40, 2020

Volume 39, 2019

Volume 38, 2018

Volume 37, 2017

Volume 36, 2016

Volume 35, 2015

Volume 34, 2014

Volume 33, 2013

Volume 32, 2012

Volume 31, 2011

Volume 30, 2011

Volume 29, 2011

Volume 28, 2010

Volume 27, 2010

Volume 26, 2010

Volume 25, 2009

Volume 24, 2009

Volume 23, 2009

Volume 22, 2008

Volume 21, 2008

Volume 20, 2008

Volume 19, 2007

Volume 18, 2007

Volume 17, 2007

Volume 16, 2006

Volume 15, 2006

Volume 14, 2006

Volume 13, 2005

Volume 12, 2005

Volume 11, 2004

Volume 10, 2004

Volume 9, 2003

Volume 8, 2002

Volume 7, 2001

Volume 6, 2000

Volume 5, 1999

Volume 4, 1998

Volume 3, 1997

Volume 2, 1996

Volume 1, 1995

Discrete and Continuous Dynamical Systems

January 1995 , Volume 1 , Issue 1

Select all articles


Chain recurrence in surface flows
Michel Benaim and Morris W. Hirsch
1995, 1(1): 1-16 doi: 10.3934/dcds.1995.1.1 +[Abstract](2656) +[PDF](347.9KB)
We investigate the topological and dynamical structure of internally chain recurrent sets for surface flows having particularly simple limit sets, including planar flows with finitely many equilibria. We verify a conjecture of Thieme (1992) concerning the limit sets of planar asymptotically autonomous equations.
Controllability of systems of interconnected membranes
John E. Lagnese
1995, 1(1): 17-33 doi: 10.3934/dcds.1995.1.17 +[Abstract](2457) +[PDF](209.4KB)
The problems of approximate, and exact, controllability of the transient behavior of a system of interconnected, two-dimensional elastic membranes in three dimensional space are considered. The membranes may have differing material properties. Control inputs and outputs are assumed to be restricted to the outer edges of the network and to the junction regions where two or more membranes are joined. The object is to characterize those membrane configurations which are approximately, or exactly, controllable. A class of membrane configurations which may be approximately controlled from the outer edges alone is identified. In particular, any two-membrane network may be approximately controlled from an arbitrarily small open subset of the outer boundary of one of the membranes. It is further proved that under some restrictions on the geometries of the individual membranes and the overall configuration, exactly controllability may be achieved through the action of controls along both the outer boundaries and in the junction regions of the network.
Diffusive epidemic models with spatial and age dependent heterogeneity
W. E. Fitzgibbon, M.E. Parrott and Glenn Webb
1995, 1(1): 35-57 doi: 10.3934/dcds.1995.1.35 +[Abstract](3317) +[PDF](236.6KB)
An epidemic model is analyzed which allows for the spatial spread of individuals within a geographical region and the incubation of the disease within infected individuals. The spatial spread of the disease is modelled by diffusion processes. The incubation period of infectives is modelled by infection-age structure. Results are established which provide qualitative prediction of the development of the epidemic in terms of spatially dependent and age dependent parameters.
Semilinear degenerate parabolic systems and distributed capacitance models
Brooke L. Hollingsworth and R.E. Showalter
1995, 1(1): 59-76 doi: 10.3934/dcds.1995.1.59 +[Abstract](2629) +[PDF](231.1KB)
A two-scale microstructure model of current flow in a medium with continuously distributed capacitance is extended to include nonlinearities in the conductance across the interface between the local capacitors and the global conducting medium. The resulting degenerate system of partial differential equations is shown to be in the form of a semilinear parabolic evolution equation in Hilbert space. It is shown directly that such an equation is equivalent to a subgradient flow and, hence, displays the appropriate parabolic regularizing effects. Various limiting cases are identified and the corresponding convergence results obtained by letting selected parameters tend to infinity.
The maximum principle for linear infinite dimensional control systems with state constraints
H. O. Fattorini
1995, 1(1): 77-101 doi: 10.3934/dcds.1995.1.77 +[Abstract](3119) +[PDF](263.1KB)
We prove a version of Pontryagin's maximum principle for linear infinite dimensional control systems (including point target conditions and state constraints). This result covers some examples for which no nonlinear theory is available at present.
A priori bounds and periodic solutions for a class of planar systems with applications to Lotka-Volterra equations
Tongren Ding, Hai Huang and Fabio Zanolin
1995, 1(1): 103-117 doi: 10.3934/dcds.1995.1.103 +[Abstract](2868) +[PDF](201.1KB)
The existence of periodic solutions for some planar systems is investigated. Applications are given to positive solutions for a class of Kolmogorov systems generalizing a predator - prey model for the dynamics of two species in a periodic environment.
Feedback control of noise in a 2-D nonlinear structural acoustics model
H. T. Banks and R.C. Smith
1995, 1(1): 119-149 doi: 10.3934/dcds.1995.1.119 +[Abstract](2989) +[PDF](2261.7KB)
A time domain feedback control methodology for reducing sound pressure levels in a nonlinear 2-D structural acoustics application is presented. The interior noise in this problem is generated through vibrations of one wall of the cavity (in this case a beam), and control is implemented through the excitation of piezoceramic patches which are bonded to the beam. These patches are mounted in pairs and are wired so as to create pure bending moments which directly affect the manner in which the structure vibrates. Th application of control in this manner leads to an unbounded control input term and the implications of this are discussed. The coupling between the beam vibrations and the interior acoustic response is inherently nonlinear, and this is addressed when developing a control scheme for the problem. Gains for the problem are calculated using a periodic LQR theory and are then fed back into the nonlinear system with results being demonstrated by a set of numerical examples. In particular, these examples demonstrate the viability of the method in cases involving excitation involving a large number of frequencies through both spatially uniform and nonuniform exterior forces.

2021 Impact Factor: 1.588
5 Year Impact Factor: 1.568
2021 CiteScore: 2.4




Special Issues

Email Alert

[Back to Top]