content_image/312863.jpg content_image/312862.jpg content_image/312864.jpg content_image/312865.jpg content_image/312866.jpg content_image/312867.jpg content_image/312868.jpg
Therefore, by means of (6.7), we have 

<img src='content_image/312863.jpg'>

<img src='content_image/312862.jpg'>

for t ∈ [ θ, θ + τ ] . 

One can find numbers s$_{1}$, s$_{2}$, s$_{3}$ ∈ [ θ, θ + τ ] such that 

<img src='content_image/312864.jpg'>

Inequality (6.8) yields 

<img src='content_image/312865.jpg'>

Let us define the function f : R 3 → R 3 as f ( v ) = ( − σv$_{1}$ + σv$_{2}$, − v$_{1}$v$_{3}$ + rv$_{1}$ − v$_{2}$, v$_{1}$v$_{2}$ − bv$_{3}$ ) , where v = ( v$_{1}$, v$_{2}$, v$_{3}$ ) . One can confirm the presence of a positive number L$_{f}$ such that ‖ f ( v ) − f ( v ) ‖ ≤ L$_{f}$ ‖ v − v ‖ for all v, v ∈ U . The relation 

<img src='content_image/312866.jpg'>

implies that 

According to the last inequality we have that 

Therefore, max t ∈ [ θ,θ + τ $_{]}$‖ y ( t ) − y ( t ) ‖ > τL$_{g}$ϵ$_{0}$ 6(2 + τL$_{f}$ ) . 

<img src='content_image/312867.jpg'>

<img src='content_image/312868.jpg'>

