State-extension modulation yields infinite attractors

Initial condition-related coexisting behavior is one of the significant features of specific chaotic systems, which corresponds to the complicated coexistences of multiple attractors or infinite attractors. To modulate the three outputs of the Chua’s system to generate infinite attractors, this paper proposes a state-extension approach via introducing the three outputs to extra dimensions through a simple integral without or with self-feedback. In comparison with most existing initial condition-controlled offset-boostable systems with discontinuous step-boost-type coexisting attractors, this approach has two important features, i.e., the seed Chua’s system is kept unchanged, and infinite continuous offset-boosted attractors or infinite continuous space-scaled attractors can be generated via configuring different initial conditions of the extra introduced variables. Both numerical study and circuit simulation confirmed the feasibility of the design.