Examples of transverse homoclinic orbits in delay equations
Non-Linear Analysis
Great delay in a predator-prey model
Non-Linear Analysis
Stiff computation
Topics in matrix analysis
Generalized variation-of-constants formula for nonlinear functional differential equations
Applied Mathematics and Computation
Delay differential equations and dynamical systems
Delay differential equations and dynamical systems
A Practical Upper Bound for Departure from Normality
SIAM Journal on Matrix Analysis and Applications
Pitfalls in Parameter Estimation for Delay Differential Equations
SIAM Journal on Scientific Computing
Global Dissipativity for A-Stable Methods
SIAM Journal on Numerical Analysis
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Pseudospectra of Linear Operators
SIAM Review
On exponential stability of nonlinear systems with delaying argument
Nonlinear Analysis: Theory, Methods & Applications
The Lyapunov functionals for delay Lotka-Volterra-type models
SIAM Journal on Applied Mathematics
SIAM Journal on Matrix Analysis and Applications
Retarded differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Differential calculus for some p-norms of the fundamental matrix with applications
Journal of Computational and Applied Mathematics
Stability of Finite and Infinite Dimensional Systems
Stability of Finite and Infinite Dimensional Systems
Cyclic Feedback Systems
Deterministic and Stochastic Time-Delay Systems
Deterministic and Stochastic Time-Delay Systems
Differential calculus for p-norms of complex-valued vector functions with applications
Journal of Computational and Applied Mathematics
Nonlinear Systems Analysis
Stability of Time-Delay Systems
Stability of Time-Delay Systems
Convergence of Multistep Time Discretizations of Nonlinear Dissipative Evolution Equations
SIAM Journal on Numerical Analysis
Continuation of Bifurcations in Periodic Delay-Differential Equations Using Characteristic Matrices
SIAM Journal on Scientific Computing
Pseudospectra and delay differential equations
Journal of Computational and Applied Mathematics
Rival approaches to mathematical modelling in immunology
Journal of Computational and Applied Mathematics
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Some aspects of causal & neutral equations used in modelling
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Sense from sensitivity and variation of parameters
Applied Numerical Mathematics
Numerical bifurcation analysis of immunological models with time delays
Journal of Computational and Applied Mathematics - Special issue: Mathematics applied to immunology
Journal of Computational and Applied Mathematics
A novel approach to exponential stability of nonlinear systems with time-varying delays
Journal of Computational and Applied Mathematics
Time-delay systems: an overview of some recent advances and open problems
Automatica (Journal of IFAC)
Hi-index | 0.00 |
Models of phenomena that evolve with time, notably those in bioscience, may be more realistic as scientific models if they incorporate a memory or time-lag rather than assume instantaneous effects. The differences and similarities between the two types of model, having regard to their 'faithfulness' as models, the sensitivity, stability, and qualitative behaviour of their solutions, are often discussed through canonical models or suggested paradigms using various 'mathematical toolkits'. We offer insight (largely self-contained, but supplemented by a bibliography) into mathematical models with time-lag and we consider how appropriate or limited are various exemplars when used as paradigms. We also mention possibilities for extending the application of the mathematical tools at our disposal.