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Noise play a creative role in the evolution of periodic and complex systems which are essential for continuous performance of the system. The interaction of noise generated within one component of a chaotic system with other component in a linear or nonlinear interaction is crucial for system performance and stability. These types of noise are inherent, natural and insidious. This study investigates the effect of state-dependent noise on the bifurcation of two chaotic systems. Circuit realization of the systems were implemented. Numerical simulations were carried out to investigate the influence of state dependent noise on the bifurcation structure of the Chen and Arneodo-Coullet fractional order chaotic systems. Results obtained showed that state dependent noise inhibit the period doubling cascade bifurcation structure of the two systems. These results poses serious challenges to system reliability of chaotic systems in control design, secure communication and power systems.
In this paper, synchronization of fractional order Coullet system with precise and also unknown parameters are studied. The proposed method which is based on the adaptive backstepping, has been developed to synchronize two chaotic systems with the sa
We use the Smaller Alignment Index (SALI) to distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian flows. This distinction is based on the different behavior of the SALI for the two cases: the index fluctuates aroun
Discrete fractional order chaotic systems extends the memory capability to capture the discrete nature of physical systems. In this research, the memristive discrete fractional order chaotic system is introduced. The dynamics of the system was studie
The relation between the onset of chaos and critical phenomena, like Quantum Phase Transitions (QPT) and Excited-State Quantum Phase transitions (ESQPT), is analyzed for atom-field systems. While it has been speculated that the onset of hard chaos is
It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the behavior of the power spectrum of the excitation energy fluctuations, which is different f