Synchronization in Coupled Multistable Systems with Hidden Attractors

Pm, Gokul; Kapitaniak, Tomasz

doi:10.1155/2017/5214235

Cited by 4 publications

(1 citation statement)

References 33 publications

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“…The literature reports several efforts regarding the synchronization of chaotic systems in the presence of hidden attractors. One of the most-used controls is feedback control with complete error [ 16 , 21 , 22 , 23 ], synchronizing with one or two state variables with the master–slave and bidirectional approach [ 20 , 24 ]. To use this control, it is necessary to adjust the coupling parameter to achieve synchronization.…”

Section: Related Workmentioning

confidence: 99%

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Zaqueros-Martinez

Gómez

Tlelo‐Cuautle

et al. 2023

Entropy

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Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi–Sugeno (T–S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance.

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Section: Related Workmentioning

confidence: 99%

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Zaqueros-Martinez

Gómez

Tlelo‐Cuautle

et al. 2023

Entropy

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Chimera states in networks of type-I Morris-Lecar neurons

et al. 2018

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Dynamic Behaviors in Coupled Neuron System with the Excitatory and Inhibitory Autapse under Electromagnetic Induction

Jia

Kirunda

et al. 2018

Complexity

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The induced current produced by electromagnetic induction can adjust the membrane potential of neuron through the feedback of a magnetic flux-controlled memristor. We adopt the numerical simulation method with the aim of investigating the synchronous behavior in the neuronal system that is coupled by chemical and electrical synapses under electromagnetic induction. Within the improved model, the effects of electromagnetic induction on neurons are described with additive memristive current on the membrane variable, and the memristive current is dependent on the variation of magnetic flow. The simulation results show that the two coupling modes play an important role in the synchronization of the system. By increasing the chemical synaptic feedback gain, we observe a transition from mixed oscillatory to periodic state at a critical value. In addition, two Hopf bifurcation points are found with the change of the external stimuli, and the state of neuron discharge is influenced by initial values. Furthermore, there is a domain of coupling strength and feedback gain values, in which the two coupled neuron system is synchronized and longer time lag is not conducive to the system synchronization.

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Synchronization in Coupled Multistable Systems with Hidden Attractors

Cited by 4 publications

References 33 publications

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Chimera states in networks of type-I Morris-Lecar neurons

Dynamic Behaviors in Coupled Neuron System with the Excitatory and Inhibitory Autapse under Electromagnetic Induction

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