Synchronization of fractional‐order chaotic systems with disturbances via novel fractional‐integer integral sliding mode control and application to neuron models

Vafaei, Vajiheh; Kheiri, Hossein; Akbarfam, A. Jodayree

doi:10.1002/mma.5548

Cited by 24 publications

(13 citation statements)

References 25 publications

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“…Similar to the Hopfield neural network, the Hindmarsh-Rose neuron is quite useful, for example: using the Hindmarsh-Rose neuron model, the authors in [16] showed that in the parameter region close to the bifurcation value, where the only attractor of the system is the limit cycle of tonic spiking type, the noise can transform the spiking oscillatory regime to the bursting one. The fractional-order version of the Hindmarsh-Rose neuron was used in [17], for the synchronization of fractional-order chaotic systems. In [18], based on two-dimensional Hindmarsh-Rose neuron and non-ideal threshold memristor, a five-dimensional neuron model of two adjacent neurons coupled by memristive electromagnetic induction, was introduced.…”

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confidence: 99%

Chaotic Image Encryption Using Hopfield and Hindmarsh–Rose Neurons Implemented on FPGA

Tlelo‐Cuautle

Díaz-Muñoz

González-Zapata

et al. 2020

Sensors

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Chaotic systems implemented by artificial neural networks are good candidates for data encryption. In this manner, this paper introduces the cryptographic application of the Hopfield and the Hindmarsh-Rose neurons. The contribution is focused on finding suitable coefficient values of the neurons to generate robust random binary sequences that can be used in image encryption. This task is performed by evaluating the bifurcation diagrams from which one chooses appropriate coefficient values of the mathematical models that produce high positive Lyapunov exponent and Kaplan-Yorke dimension values, which are computed using TISEAN. The randomness of both the Hopfield and the Hindmarsh-Rose neurons is evaluated from chaotic time series data by performing National Institute of Standard and Technology (NIST) tests. The implementation of both neurons is done using field-programmable gate arrays whose architectures are used to develop an encryption system for RGB images. The success of the encryption system is confirmed by performing correlation, histogram, variance, entropy, and Number of Pixel Change Rate (NPCR) tests.In [2] J.J. Hopfield introduced the neuron model that nowadays is known as the Hopfield neural network. Ten years later, a modified model of Hopfield neural network was proposed in [3], and applied in information processing. Immediately, the Hopfield neural network was adapted to generate chaotic behavior in [4] where the authors explored bifurcation diagrams. In [5] the simplified Hopfield neuron model was designed to use a sigmoid as activation function, and three neurons were used to generate chaotic behavior. In addition, the authors performed an optimization process updating the weights of the neurons interconnections. The Hopfield neuron was combined with a chaotic map in [6] to be applied in chaotic masking. More recently, the authors in [7] proposed an image encryption algorithm using the Hopfield neural network. In the same direction, the authors in [8] detailed the behavior of Hindmarsh-Rose neuron to generate chaotic behavior. Its bifurcation diagrams were described in [9], and the results were used to select the values of the model to improve chaotic behavior. Hindmarsh-Rose neurons were synchronized in [10], optimizing the scheme of Lyapunov function with two gain coefficients. In this way, the synchronization region is estimated by evaluating the Lyapunov stability. Two Hindmarsh-Rose neurons were synchronized in [11], and the system was used to mask information in continuous time. To show that the neurons generate chaotic behavior, one must compute Lyapunov exponents, and for the Hindmarsh-Rose neuron they were evaluated by the TISEAN package in [12].The Hopfield neural network has been widely applied in chaotic systems [13][14][15]. This network consists of three neurons, and the authors in [13] proposed a simplified model by removing the synaptic weight connection of the third and second neuron in the original Hopfield network. Numerical simulations were carried out considering values from t...

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confidence: 99%

Chaotic Image Encryption Using Hopfield and Hindmarsh–Rose Neurons Implemented on FPGA

Tlelo‐Cuautle

Díaz-Muñoz

González-Zapata

et al. 2020

Sensors

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“…Chaotic systems are applicable in a wide range of research classifications such as jerk systems [1,2], robotics [3,4], neuron models [5,6], oscillators [7,8], circuits [9][10][11], biological systems [12,13], chemical systems [14,15], and memristors [16,17]. In view of their attractive triangular structure, considerable numbers of papers have been published on the chaos jerk models [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

A simple multi-stable chaotic jerk system with two saddle-foci equilibrium points: analysis, synchronization via backstepping technique and MultiSim circuit design

Sambas¹,

Vaidyanathan

Moroz

et al. 2021

IJECE

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<span>This paper announces a new three-dimensional chaotic jerk system with two saddle-focus equilibrium points and gives a dynamic analysis of the properties of the jerk system such as Lyapunov exponents, phase portraits, Kaplan-Yorke dimension and equilibrium points. By modifying the Genesio-Tesi jerk dynamics (1992), a new jerk system is derived in this research study. The new jerk model is equipped with multistability and dissipative chaos with two saddle-foci equilibrium points. By invoking backstepping technique, new results for synchronizing chaos between the proposed jerk models are successfully yielded. MultiSim software is used to implement a circuit model for the new jerk dynamics. A good qualitative agreement has been shown between the MATLAB simulations of the theoretical chaotic jerk model and the MultiSIM results</span>

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“…According to the biological characteristics of neurons, the types of synchronization for neuron systems include GPS [26], [27], complete synchronization (CS) [25], [28], lag synchronization (LS) [29], anti-phase synchronization (APS) [30], and generalized function projective synchronization (GFPS) [31]. For the nonlinear and chaotic characteristics of neuronal models, various control methods have been applied in the synchronization of neurons, such as feedback control, neural network control, adaptive control, and slide mode control, by using the linear matrix inequality and Lyapunov theory [25], [28], [29], [32]- [34].…”

Section: Introductionmentioning

confidence: 99%

“…For HR neuron systems subject to asymmetrical time delays, Fan et al discussed how the time delays and coupling strengths affected the lag synchronization and transmission of firing modes between neurons [29]. Vajiheh et al introduced a sliding mode technique for GPS in fractional-order systems and implemented it in classical HR neuronal models [31].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Fuzzy Control for the Generalized Projective Synchronization of Fractional-Order Extended Hindmarsh-Rose Neurons

2020

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We investigate the generalized projective synchronization (GPS) control of fractional-order extended Hindmarsh-Rose (FOEHR) neuronal models with transcranial magneto-acoustical stimulation (T-MAS) input. This improved neuronal model has advantages in describing the complex firing characteristics of neurons stimulated by alternating current. In this study, a master-slave neuron system consisting of two FOEHR neuronal models is assumed to be subject to uncertain model parameters and unknown external disturbances. To quantify the GPS error, we design a new error variable based on the properties of the fractional-order derivative and construct a related GPS error system. Fuzzy logic systems are introduced to approximate the unknown nonlinear dynamics of the error system. To ensure the synchronous firing rhythms of the master-slave neuron system, an adaptive fuzzy control algorithm is proposed under the Lyapunov approach, in which the adaptive parameters are robust to the estimation errors. By choosing the appropriate design parameters, the proposed control scheme enables the master-slave neuron system to achieve GPS in a finite amount of time and to be resilient to uncertain parameters and unknown disturbances. The simulation results demonstrate that after the designed control inputs are implemented, the states of the slave neuron synchronize with those of the master neuron in specified proportions, and the corresponding synchronization error converges towards an arbitrarily small neighborhood of zero. INDEX TERMS Generalized projective synchronization, fractional-order, extended Hindmarsh-Rose neuronal model, fuzzy logic system.

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Synchronization of fractional‐order chaotic systems with disturbances via novel fractional‐integer integral sliding mode control and application to neuron models

Cited by 24 publications

References 25 publications

Chaotic Image Encryption Using Hopfield and Hindmarsh–Rose Neurons Implemented on FPGA

Chaotic Image Encryption Using Hopfield and Hindmarsh–Rose Neurons Implemented on FPGA

A simple multi-stable chaotic jerk system with two saddle-foci equilibrium points: analysis, synchronization via backstepping technique and MultiSim circuit design

Adaptive Fuzzy Control for the Generalized Projective Synchronization of Fractional-Order Extended Hindmarsh-Rose Neurons

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