## Recent Advances in Delay Differential and Difference EquationsDelay differential and difference equations serve as models for a range of processes in biology, physics, engineering and control theory. In this volume, the participants of the International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary, July 15-19, 2013 present recent research in this quickly-evolving field. The papers relate to the existence, asymptotic and oscillatory properties of the solutions; stability theory; numerical approximations; and applications to real world phenomena using deterministic and stochastic discrete and continuous dynamical systems. |

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### Contents

1 | |

2 Comparison Theorems for SecondOrder Functional Differential Equations | 86 |

3 Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems Using Transformations | 105 |

4 Almost Oscillatory Solutions of Second Order Difference Equations of Neutral Type | 120 |

5 Uniform Weak Disconjugacy and Principal Solutions for Linear Hamiltonian Systems | 131 |

6 Stability Criteria for Delay Differential Equations | 161 |

7 Analyticity of Solutions of Differential Equations with a Threshold Delay | 172 |

8 Application of Advanced Integrodifferential Equations in Insurance Mathematics and Process Engineering | 181 |

9 Stability and Control of Systems with Propagation | 197 |

10 Discrete Itô Formula for Delay Stochastic Difference Equations with Multiple Noises | 219 |

11 On Semilinear Hyperbolic Functional Equations with StateDependent Delays | 233 |

12 A Fast Parallel Algorithm for Delay Partial Differential Equations Modeling the Cell Cycle in Cell Lines Derived from Human Tumors | 251 |

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### Other editions - View all

Recent Advances in Delay Differential and Difference Equations Ferenc Hartung,Mihaly Pituk No preview available - 2014 |

Recent Advances in Delay Differential and Difference Equations Ferenc Hartung,Mihaly Pituk No preview available - 2014 |

Recent Advances in Delay Differential and Difference Equations Ferenc Hartung,Mihaly Pituk No preview available - 2016 |

### Common terms and phrases

ˇ ˇ Appleby applied asymptotic behaviour asymptotic stability cell coefficients consider continuous and obeys continuous functions convergence corresponding dB(s defined Delay Differential delay differential equations denote density function derivative difference equations dynamics ensures exists exponential f is continuous finite follows functional differential equations globally half-linear Hamiltonian systems Hence holds implies inequality initial conditions intermediate solutions Itô formula jx.t/jC Lemma lim sup linear Hamiltonian systems Lipschitz continuous Lyapunov functional MAL-CRN Math matrix solution matrix-valued function nonlinear nonnegative obtain ordinary differential equations oscillation oscillatory paper parameters perturbed polynomial positive Proof of Theorem properties prove QP system random variables regularly varying Remark resp result satisfies sequence ſº solution of 1.2 stochastic stochastic differential equations Suppose that f taking values tºo uniform weak disconjugacy uniformly weakly disconjugate unique University of Pannonia zero