Search results for "lattice dynamical systems"

showing 5 items of 5 documents

Attractors for non-autonomous retarded lattice dynamical systems

2015

AbstractIn this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.

Statistics and ProbabilityDifferential equations with delayDynamical systems theoryNon-autonomous systemslattice dynamical systemsPullback attractorHamiltonian systemLinear dynamical systemProjected dynamical systemAttractorQA1-939pullback attractorMathematicsNumerical AnalysisApplied MathematicsMathematical analysisdifferential equations with delaynon-autonomous systemsClassical mechanicsLattice dynamical systemsPullback attractorset-valued dynamical systemsSet-valued dynamical systemsLimit setRandom dynamical systemMathematicsAnalysis
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On a Retarded Nonlocal Ordinary Differential System with Discrete Diffusion Modeling Life Tables

2021

In this paper, we consider a system of ordinary differential equations with non-local discrete diffusion and finite delay and with either a finite or an infinite number of equations. We prove several properties of solutions such as comparison, stability and symmetry. We create a numerical simulation showing that this model can be appropriate to model dynamical life tables in actuarial or demographic sciences. In this way, some indicators of goodness and smoothness are improved when comparing with classical techniques.

General Mathematicslattice dynamical systemslife tables010103 numerical & computational mathematics:CIENCIAS ECONÓMICAS [UNESCO]01 natural sciencesStability (probability)010104 statistics & probabilitydiscrete nonlocal diffusion problemsComputer Science (miscellaneous)Applied mathematics0101 mathematicsDiffusion (business)Engineering (miscellaneous)MathematicsDiffusion modelingSmoothness (probability theory)Computer simulationlcsh:MathematicsUNESCO::CIENCIAS ECONÓMICASlcsh:QA1-939Symmetry (physics)Ordinary differential systemordinary differential equationsOrdinary differential equationretarded equationsMathematics
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Random attractors for stochastic lattice systems with non-Lipschitz non-linearity

2012

In this paper we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.

Stochastic lattice dynamical systemsrandom attractorset-valued dynamical system
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Asymptotic Behaviour of a Logistic Lattice System

2014

In this paper we study the asymptotic behaviour of solutions of a lattice dynamical system of a logistic type. Namely, we study a system of in nite ordinary di erential equations which can be obtained after the spatial discretization of a logistic equation with di usion. We prove that a global attractor exists in suitable weighted spaces of sequences.

Lattice dynamical systemsglobal attractorlogistic equation
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On Differential Equations with Delay in Banach Spaces and Attractors for Retarded Lattice Dynamical Systems

2014

In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation in a Banach space by assuming that the nonlinear term is in some sense weakly continuous. We then apply this result to a lattice dynamical system with delay, proving also the existence of a global compact attractor for such system.

Lattice dynamical systemsset-valued dynamical systemsdifferential equations with delayglobal attractor
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