A snail-shaped chaotic system with large bandwidth: dynamical analysis, synchronization and secure communication scheme

Abstract

In this paper, a snail-shaped chaotic system with large bandwidth is first introduced, it contains two quadratic, one cubic and two quartic nonlinear terms. The new snail-shaped autonomous system can exhibit periodic, quasi-periodic and chaotic behaviors with the variations of its parameters. The major properties of the proposed model are discussed using equilibrium points, Kaplan–Yorke dimension, Lyapunov exponents spectrum and bifurcation diagrams. The feasibility of the snail-shaped system is verified by implementing an electronic circuit via Multisim software. The obtained results proving the complex chaotic behavior of the new system, which make it very desirable to use in many fields of engineering especially in secure communication. Also, synchronization between the snail-shaped chaotic system and the Rossler hyperchaotic system is achieved. Finally, a new simple secure communication scheme is developed based on the proposed system and using drive response synchronization in order to prove the success of the new system to complete the encryption/decryption process.