Synchronization transitions in a discrete memristor-coupled bi-neuron model

Li, Kexin; Bao, Bocheng; Ma, Jun; Chen, Mo; Bao, Han

doi:10.1016/j.chaos.2022.112861

Cited by 51 publications

(6 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[24][25][26][27] Due to the non-volatile, nanoscale, memory properties of memristors, and the similarity between nano-scale moving particles in memristors and mobile neu-rotransmitters in biological synapses, memristors are often considered as ideal candidates for simulating synapses. [28][29][30][31][32] For example, Bao et al [33] established a discrete neuron network containing two identical Rulkov neurons, and regarded the current flowing through the memristor as the electromagnetic induction current to analyze the effect of electromagnetic induction on the dynamic behavior of neuron network. Under the influence of the electromagnetic induction current, the model can achieve complete synchronization and lag synchronization.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Yan 晏,

Li 李,

Li 李

2024

Chinese Phys. B

View full text Add to dashboard Cite

Research on discrete memristor-based neural networks has received much attention. However, current research mainly focuses on memristor–based discrete homogeneous neuron networks, while memristor-coupled discrete heterogeneous neuron networks are rarely reported. In this study, a new four-stable discrete locally active memristor is proposed and its nonvolatile and locally active properties are verified by its power-off plot and DC V-I diagram. Based on two-dimensional discrete Izhikevich neuron and two-dimensional discrete Chialvo neuron, a heterogeneous discrete neuron network is constructed by using the proposed discrete memristor as a coupling synapse connecting the two heterogeneous neurons. Considering the coupling strength as the control parameter, chaotic firing, periodic firing and hyperchaotic firing patterns are revealed. In particular, multiple coexisting firing patterns are observed, which are induced by different initial values of the memristor. Phase synchronization between the two heterogeneous neurons is discussed and it is found that they can achieve perfect synchronous at large coupling strength. Furthermore, the effect of Gaussian white noise on synchronization behaviors is also explored. We demonstrate that the presence of noise not only leads to the transition of firing patterns, but also achieves the phase synchronization between two heterogeneous neurons under low coupling strength.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Yan 晏,

Li 李,

Li 李

2024

Chinese Phys. B

View full text Add to dashboard Cite

show abstract

“…Analogue circuit realization of discrete memristors is reported in [18]. Discrete neuron model is proposed [19] and synchronization transitions is investigated [20]. Lai and Yang develop a discrete neuron network [21] while BP neural network is presented in [22].…”

Section: Introductionmentioning

confidence: 99%

Applying exponential unit for breaking symmetry of memristive maps

Phu Thoai,

Volos,

Vincenzo Radogna

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

The emergence of memristors has piqued significant interest in memristive maps due to their unique characteristics. In this paper, we introduce a novel and effective method for constructing memristor maps, leveraging the power of exponential units. Interestingly, the incorporation of these exponential units disrupts symmetry and alters the count of fixed points within the map. The method is simple to build maps with chaos and higher order maps. These make our work different from existing methods. To demonstrate the efficacy of our approach, we have focused our attention on examining the dynamics, feasibility, and practical applications of a specific map, referred to as the EPMM1 map. Furthermore, we show that by extending this approach, it becomes straightforward to create other innovative memristive maps, including those with multiple memristors.

show abstract

“…In the recent decade, the heterogeneity can improve the task performance in promoting robust learning [20]. A bidirectionally coupled two Rulkov maps, composed of two map neurons has infinitely many fixed points with coexisting multiple firing patters [21]. A two-neuron network is established by coupling two Morris-Lecar neurons using a memristor synapse and shown to devellop chaotic behaviors [22].…”

Section: Introductionmentioning

confidence: 99%

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Madasamy,

Boui a Boya,

Kengne

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

This work deals with the regular and chaotic dynamics of a system made up of two Hopfield-type neurons with two different activation functions: the hyperbolic tangent function and the Crespi function. The mathematical model is in the form of an autonomous differential system of order four with odd symmetry. The analysis highlights nine equilibrium points and four of these points experience a Hopf bifurcation at the same critical value of a control parameter which can be either the diss1ipation parameter or one of the coupling coefficients. This makes plausible the presence of four parallel bifurcation branches as well as the coexistence of multiple attractors in the behavior of the system. One of the highlights revealed in this work is the coexistence of three double-scroll type attractors of particular topology as well as the presence of a four-spiral attractor. Furthermore, the coexistence of both self-excited and hidden dynamics is also reported. All this plethora of dynamics is elucidated by making use of the usual tools for analyzing nonlinear systems such as bifurcation diagrams, the maximum of Lyapunov exponent, basins of attractions as well as phase portraits. A physical implementation of the microcontroller-based system is envisaged in order to confirm the plethora of behaviors observed theoretically.

show abstract

Synchronization transitions in a discrete memristor-coupled bi-neuron model

Cited by 51 publications

References 51 publications

Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Applying exponential unit for breaking symmetry of memristive maps

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Contact Info

Product

Resources

About