A Generalized 2-D Model for Fully Bounded Chaotic Attractors and Chaotic Seas

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A Fully Bounded 2-D Model For Chaotic Attractors Or Chaotic Seas

In this paper, we propose the following 2-D map as a model for a fully bounded map:

(1) where is the bifurcation parameter. The map (1) is characterized by three nonlinearities and These functions must satisfy the conditions:

with for all and some values of . Assume also that the values of the functions ) and are finite for all . The map (1) is dissipative when for allotherwise the map is conservative.