Varying the parameters c1 and Lambda


(with reference to the c1,lambda plane)

First Quadrant:

If the values of C1>0 and the values of lambda>0 then the parameters are considered to be in the first quadrant. All of the values that were run with in the quadrant were held greater than zero but less than orequal to 3. These parameters resulted in a shock moving with a steady periodic motion. The parameters also made the forcing terms go to a steady periodic function independent of the initial conditions. For all the conditions tried both the movement and the forcing system exhibited single period behavior.
(.1,.1)
(.1,1.5)
(.1,3)
(.75,1.5)
(1.25,3)
(1.5,.1)
(.1,.75)
(.75,.1)

Second Quadrant

If the values of C1>0 and the values of lambda<0 then the parameters are considered to be in the second quadrant. These parameters resulted in more interesting behavior including chaos. Although for all the conditions tried both the movement and the forcing system exhibited single period behavior.
(-.1,.1)
(-.1,1)
(-1,.1)
(-1,2)
"
Third Quadrant

If the values of C1<0 and the values of lambda<0 then the parameters are considered to be in the third quadrant. All of the values that were run with in the quadrant were held less than zero but greater than or equal to -1.5 These parameters resulted in a shock moving with a steady periodic motion but this motion was caused from residence. This is true because as time increases the forcing term dies out and there is nothing driving the system, but it continues to run. For all the conditions tried both the movement and the forcing system exhibited single period behavior.
(-1,-1)
(-.75,-.75)
(-.75,-1.5)
(-.5,-.5)

Fourth Quadrant

If the values of C1>0 and the values of lambda<0 then the parameters are considered to be in the fourth quadrant. These parameters resulted in a shock moving with a steady periodic motion but this motion was caused from residence for the first two cases but the last cases the motion just seceded as the forcing term dies. The first two cases show residence because as time increases the forcing term dies out and there is nothing driving the system, but it continues to run. For all the conditions tried both the movement and the forcing system exhibited single period behavior.
(.1,-.75)
(.75,-.1)
(1.5,-1.5)
(.1,-.1)
(.1,-1.5)
(1.5,-.1)







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