A family of memristive multibutterfly chaotic systems with multidirectional initial-based offset boosting

Memristors are commonly used to construct memristive chaotic systems with complex dynamics because of their strong nonlinearity and unique memory effects. In this paper, a simplified multi-piecewise memristor is applied for designing a family of memristive multibutterfly chaotic systems (MMBCSs). By coupling different numbers of the simplified multi-piecewise memristors into a modified Sprott C system, three MMBCSs are constructed. Theoretical analysis and numerical simulations show that the three MMBCSs can not only generate connected 1D(direction)-, 2D(plane)-, and 3D(space)-multibutterfly chaotic attractors (MBCAs), respectively, but also can respectively produce unconnected 1D-, 2D-, and 3D-MBCAs. Also, the number and position of butterfly attractors can be easily controlled by switching the memristor’s integer parameters and initial states, respectively. More importantly, the constructed three MMBCSs exhibit different initial-based offset boosting including 1D-, 2D-, and 3D-boosting behaviors, respectively. Especially, the 3D-initial-offset behavior is found in chaotic systems at the first time. Furthermore, we further implement the physical circuit of the three MMBCSs, and various typical dynamical behaviors are demonstrated by hardware experiments and Multisim simulations. Finally, a medical image encryption solution for online medical treatment is designed based on the proposed MMBCSs.