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This paper presents a study of the phenomenon of extreme multi-stability in a novel 4D hyperjerk memristive system. The proposed system appertains to the category of dynamical systems with hidden attractors due to infinite equilibrium points. The behaviour of the system is investigated through numerical simulations, by using well-known tools of nonlinear theory, such as phase portrait, bifurcation diagram and Lyapunov exponents. Also, this work showed that the extreme multi-stability phenomenon of the behaviour of infinitely many coexisting attractors depends on the initial conditions of the variables of the system. Moreover, the case of chaos synchronisation of the system with unknown parameters, using adaptive synchronisation method, is investigated.

In recent years, information security requires randomly selected strong keys. Most of the proposed methods provide keys, which are based on chaotic cryptographic algorithms. In this paper, a fingerprint image encryption scheme, based on a chaotic true random bit generator (TRBG), is proposed. The chaotic generator is based on a non-linear electronic circuit, which produces double scroll chaotic attractors. The initial conditions and the values of the circuit parameters serve as the private key of the cryptographic scheme. We use two chaotic generators with different initial conditions, which produce the bits sequences that XOR-ed for generating the final bits sequence. A well known statistical suite for testing the distribution of the bits sequence was adopted. This sequence has been used to encrypt and decrypt the fingerprint images. Also, the security analysis of the encrypted image demonstrates the high security of the proposed encryption scheme.