Horseshoe in a class of planar mappings

Abstract

Bursting dynamics of mappings is investigated in this paper. We first present stability analysis of the mappings' equilibria with various parameters. Then for three mappings P , P ¯ , and P ^ with different parameters, we study their powers P 4 , P ¯ 6 , and P ^ 4 . We show that the mappings thus obtained are chaotic by giving a rigorous verification of existence of horseshoes in these mappings. Precisely, we prove that the mapping P ¯ 6 is semiconjugate to the 3-shift mapping; the mappings P 4 and P ^ 4 are semiconjugate to the 4-shift mapping.