Degenerate Critical Points and Catastrophes: Fold Catastrophe

time, t

1.5

perturbation, ϵ

0

θ

1

= 2π ×

0

1

8

1

4

θ

2

= 2π ×

-

1

2

-

7

16

-

3

8

-

5

16

-

1

4

-

3

16

-

1

8

-

1

16

0

ϕ

1

= π ×

1

8

1

4

3

8

1

2

ϕ

2

= π ×

1

16

1

8

3

16

1

4

5

16

3

8

7

16

1

2

The simple algebraic curve

φ(t)=

3

t

+ϵt

is a good enough example to explain degeneracy and catastrophe in the extended phase space

(t,φ(t),



φ

(t))

. With the help of this Demonstration, students can easily understand the fold catastrophe.