## A nonlinear system of differential-difference equations |

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### Contents

Existence and Uniqueness Theorems | 9 |

Boundedness of Solutions | 17 |

Series Solution Matrix I + P | 30 |

3 other sections not shown

### Common terms and phrases

A N(t a+x)cos(y assume asymptotic behavior asymptotically stable bounded region boundedness Chapter characteristic equation chosen to satisfy closed feedback loop coefficients considered constant continuous function convergence cos(y cot(y+a denotes difference equation differential-difference equations eigenvalues equation 6.8 equilibrium point existence and uniqueness exponential polynomials Figure Hence hypercube Identity matrix implies inequality initial functions integration interval least one component LEMMA limit point linear matrix equation n-dimensional n-space negative elements nonlinear oscillate parameter periodic solutions positive connection matrix positive equilibrium solution positive matrix positive real numbers positive semi-orbit C+ positive solution Proof proved reinforcing closed feedback remain bounded restrictions roots of 7.5 s)ds satisfy R(s scalar equation set L(C+ shown sin(y solution of 5.1 solution x(t strictly positive system of differential-difference system of equations Theorem 6.1 u,v-plane u+vi uik(t ulk(t uniformly bounded uniqueness theorem unit Interval variable vector-valued function Volterra equations Xi(t xlk(t xn(t