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Simple nonlinear systems

Simple nonlinear systems. Nonlinear growth of bugs and the logistic map x i+1 =μx i (1-x i ). The fix point. Bifurcation , self-similarity , and chaos. Bifurcation points converge geometrically. 3.449. 3.544, 3.5644, 3.5688. a constant.

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Simple nonlinear systems

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  1. Simple nonlinear systems

  2. Nonlinear growth of bugs and the logistic map xi+1=μxi(1-xi)

  3. The fix point

  4. Bifurcation, self-similarity, and chaos

  5. Bifurcation points converge geometrically 3.449 3.544, 3.5644, 3.5688 a constant

  6. Geometric convergence indicates that something is preserved when we change the scale(scaling property) Feigenbaum (1978) set out to calculate another iteration xi+1=μsin (xi) and got the same constant (4.6692…)! So are other 1-dim maps that have bifurcations! He discovered “universality” in nonlinear systems Note: Keith Briggs from the Mathematics Department of the University of Melbourne in Australia computed what he believes to be the world-record for the number of digits for the Feigenbaum number: 4. 669201609102990671853203820466201617258185577475768632745651 343004134330211314737138689744023948013817165984855189815134 408627142027932522312442988890890859944935463236713411532481 714219947455644365823793202009561058330575458617652222070385 410646749494284981453391726200568755665952339875603825637225

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