content_image/314765.jpg content_image/314766.jpg content_image/314767.jpg content_image/314768.jpg
Suppose that max t ∈ [ θ,θ + τ $_{]}$‖ y ( t ) − y ( t ) ‖ = ‖ y ( ξ ) − y ( ξ ) ‖ for some ξ ∈ [ θ, θ + τ ] . Define the number 

where M$_{g}$ = sup x ∈ Λ ‖ g ( x ) ‖ , and let 

For t ∈ [ θ $^{1}$, θ1 + Δ] , by favour of the equation 

<img src='content_image/314765.jpg'>

<img src='content_image/314766.jpg'>

<img src='content_image/314767.jpg'>

one can obtain that 

<img src='content_image/314768.jpg'>

The length of the interval J 1 = [ θ $^{1}$, θ$^{1}$+Δ] does not depend on x ( t ) , x ( t ) , and for t ∈ J 1 the inequality ‖ y ( t ) − y ( t ) ‖ > ϵ$_{1}$ holds, where ϵ$_{1}$ = τL$_{g}$ϵ$_{0}$ 12(2 + τL$_{f}$ ) . Consequently, the response system (2.3) is sensitive. □ 

## References 

[1] H. Poincaré, Les Methodes Nouvelles de la Mecanique Celeste, Vol. I, II, III, Paris, 1899; reprint, Dover, New York, 1957. 

[2] E.N. Lorenz, Maximum simplification of the dynamic equations, Tellus 12 (1960) 243–254. 

[3] E.N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci. 20 (1963) 130–141. 

[4] B. Saltzman, Finite amplitude free convection as an initial value problem, J. Atmos. Sci. 19 (1962) 329–341. 

[5] S. Wiggins, Global Bifurcations and Chaos, Springer, New York, 1988. 

