Implementation of chaotic circuits with a digital time-delay block

In this paper, the implementation of time-delay chaotic circuits is investigated. To implement the time-delay block, a solution based on a digital circuitry has been adopted. This solution leads to a programmable hardware which can be realized by using available field programmable gate arrays. In this paper, issues raised from this implementation such as the behavior of the system with respect to the precision and the sampling rate of the conversion process have been investigated. The synchronization error is proposed as an indicator of the accuracy of the whole implementation.     

A fractional map with hidden attractors: chaos and control

The European Physical Journal Special Topics - This paper studies the dynamics of a new fractional-order map with no fixed points. Through phase plots, bifurcation diagrams, largest Lyapunov...     

Synchronization in a multiplex network of gene oscillators

Study of the synchronization in the network of gene oscillator network has vital importance in understanding of rhythmicity of molecular and cellular activities. In this paper, we analyze a network of linearly coupled genetic oscillators in a multiplex structure. The coupling strength values are changed and the coupling range is considered to be fixed, but different in the two layers. The analyses are done in two cases of periodic and chaotic oscillations. By computing the statistical measures, the interlayer and intralayer synchronization states are studied. The results show that the layer with higher coupling range has more enhanced synchrony and is less affected by the turbulent behavior of the other layer. On the other hand, the layer with lower coupling range approaches synchronization by strengthening the interlayer and intralayer couplings. The interlayer synchronization is also achieved in high coupling strength values.     

A simple chaotic circuit with a hyperbolic sine function and its use in a sound encryption scheme

In this work, one of the most simple chaotic autonomous circuits, which has been reported in the literature, is presented. The proposed circuit, that belongs to jerk systems family, is described mathematically by a 3-D dynamical system with only five terms, and it has only one nonlinear term, which is the hyperbolic sine term implemented with two antiparallel diodes. This new jerk system presents interesting chaotic phenomena, such as coexisting attractors and antimonotonicity. Also, as an application of the proposed system a sound encryption scheme that is based on a random number generator, which is implemented with the jerk system, is presented. The practical usefulness of the proposed simple chaotic jerk circuit is confirmed from the results of NIST-800-22 tests of the chaotic random number generator, as well as from the successful sound encryption and decryption process.     

Dynamics,circuit realization,control and synchronization of a hyperchaotic hyperjerk system with coexisting attractors

Although different hyperjerk systems have been discovered, a few hyperjerk systems can exhibit hyperchaotic behavior. In this work, we introduce a new hyperjerk system with hyperchaotic attractors. By investigating dynamics of the system, we have observed the different coexisting attractors such as coexistence of period-2 attractors, or coexistence of period-2 attractor and quasiperiodic attractor. It is worth noting that this striking phenomenon is rarely reported in a hyperjerk system. The proposed system has been realized with electronic components. The agreement between the simulation and experimental results indicates the feasibility of the hyperjerk system. Moreover, chaos control and synchronization of such hyperjerk system have been also reported.     

Modeling of Neurodegenerative Diseases Using Discrete Chaotic Systems

Parkinson's and Huntington's diseases are two of the most common neurodegenerative disorders.Tremor, muscle stiffness, and slowness of movement are symptoms of Parkinson's disease. The symptoms of Huntington's disease are severe reduction in muscle control, emotional disturbance, and pathological disorders in brain cells.These diseases are caused by destruction of the cells that secrete a substance called dopamine. In this paper,a new discrete chaotic system is introduced,which can mimic the brain's behavior for neurodegenerative diseases such as Parkinson,Huntington, and Hypokinesia. This system is described based on the similarity between the brain's behavior in normal and abnormal conditions and the chaotic systems. Bifurcation analysis is carried out with respect to different parameters, providing full spectrum of the behavior for different parameter values.Our results can be used to mathematically study the mechanisms behind these diseases.     

Prediction of bifurcations by varying critical parameters of COVID-19

Nonlinear Dynamics - Coronavirus disease 2019 is a recent strong challenge for the world. In this paper, an epidemiology model is investigated as a model for the development of COVID-19. The...