Coexistence of Multiple Stable States and Bursting Oscillations in a 4D Hopfield Neural Network

Njitacke, Zeric Tabekoueng; Kengne, Jacques; Fotsin, Hilaire Bertrand

doi:10.1007/s00034-019-01324-6

Cited by 50 publications

(5 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the voltage input from the j-th neuron, its neuron activation function is ( ) tanh x j . In [34], fixed R i =1, C i =1 , I i =0 and N = 4, the model of the 4-neurons HNN with the topological connection based on these various hypotheses was shown in figure 1.…”

Section: Fractional Calculusmentioning

confidence: 99%

See 1 more Smart Citation

Design and implementation of a new fractional-order Hopfield neural network system

Zhou¹,

Wang²

2022

Phys. Scr.

View full text Add to dashboard Cite

In this work, a novel chaotic system of fractional-order based on the model of Hop-field Neural Network (HNN) is proposed. The numerical solutions of the 4-neurons-based HNN fractional-order chaotic system are obtained by using the Adomain decomposition method. The dynamical performances of the the 4-neurons-based HNN fractional-order chaotic system are explored through attractor trajectories, bifurcation diagrams, Lyapunov exponents, SE complexity and chaotic diagram based on SE complexity. In addition, the 4-neurons-based HNN fractionalorder chaotic system is circuit implemented based on the Multisim platform. The experimental results indicate that the 4-neurons-based HNN fractional-order chaotic system has rich dynamic behavior, and the influence of different order on the dynamical properties of the system are particularly great. This research will provide theoretical foundation and experimental basis for the hardware implementation and application of the 4-neurons-based HNN fractional-order chaotic system.

show abstract

Section: Fractional Calculusmentioning

confidence: 99%

“…On the base of the integrators, capacitors, operational amplifiers and resistors, the circuit design for the 4-neurons-based HNN fractional-order chaotic system is shown in figure 7, where F and tanh represent the fractional-order unit circuit and tanh unit circuit. According to [34]. The circuit design for tanh in figure 8.…”

Section: Circuit Realizationmentioning

confidence: 99%

Design and implementation of a new fractional-order Hopfield neural network system

Zhou¹,

Wang²

2022

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Bursting oscillation is one of the different types of oscillatory behavior observed in biological, physical, and chemical systems [30,[46][47][48][49]. It is characterized by the alternation of a silent phase and an active phase during each period of oscillation.…”

Section: Bursting Oscillationmentioning

confidence: 99%

On the modeling of some triodes-based nonlinear oscillators with complex dynamics: case of the Van der Pol oscillator

Tegnitsap¹,

Tsefack²,

Ngouonkadi³

et al. 2021

Phys. Scr.

View full text Add to dashboard Cite

In this work, the dynamic of the triode-based Van der Pol oscillator coupled to a linear circuit is investigated (Triode-based VDPCL oscillator). Towards this end, we present a mathematical model of the triode, chosen from among the many different ones present in literature. The dynamical behavior of the system is investigated using classical tools such as two-parameter Lyapunov exponent, one-parameter bifurcation diagram associated with the graph of largest Lyapunov exponent, phase portraits, and time series. Numerical simulations reveal rather rich and complex phenomena including chaos, transient chaos, the coexistence of solutions, crisis, period-doubling followed by reverse period-doubling sequences (bubbles), and bursting oscillation. The coexistence of attractors is illustrated by the phase portraits and the cross-section of the basin of attraction. Such triode-based nonlinear oscillators can find their applications in many areas where ultra-high frequencies and high powers are demanded (radio, radar detection, satellites communication, etc.) since triode can work with these performances and are often used in the aforementioned areas. In contrast to some recent work on triode-based oscillators, LTSPICE simulations, based on real physical consideration of the triode, are carried out in order to validate the theoretical results obtained in this paper as well as the mathematical model adopted for the triode.

show abstract

“…As a result, several mathematical models have been developed and studied in the literature to study some of the dynamical mechanisms of the brain. The Hopfield neural network model [3][4][5][6], the Hodgkin-Huxley neuron [7], the 2-D Hindmarsh-Rose (HR), the 3D-HR neuron models [8,9], the FitzHugh-Nagumo (FHN) neuron model [10,11], the MorrisLecar neuron model [12], the Chay neuron model [13], the Izhikevich neuron model [14], and the Rulkov neuron model [15] are some examples. In the same vein, several artificial synapse models for presynaptic and postsynaptic neuron coupling have been developed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation

Muni

Njitacke

Feudjio

et al. 2022

Chaos Theory and Applications

View full text Add to dashboard Cite

In this paper we have introduced and investigated the collective behavior of a network of memristive Hindmarsh-Rose (HR) neurons. The proposed model was built considering the memristive autapse of the traditional 2D HR neuron. Using the one-parameter bifurcation diagram and its corresponding maximal Lyapunov exponent graph, we showed that the proposed model was able to exhibit a reverse period doubling route to chaos, phenomenon of interior and exterior crises. Three different configurations of the ring-star network of the memristive HR neuron model, including ring-star, ring, and star, have been considered. The study of those network configurations revealed incoherent, coherent , chimera and cluster state behaviors. Coherent behavior is characterized by synchronization of the neurons of the network, while incoherent behaviors are characterized by the absence of synchronization. Chimera states refer to a differet state where there is a coexistence of synchroniaed and asynchronized nodes of the network. One of the interesting result of the paper is the prevalence of double-well chimera states in both ring and ring-star network and has been first mentioned in the case of memrisitve HR neuron model.

show abstract

Coexistence of Multiple Stable States and Bursting Oscillations in a 4D Hopfield Neural Network

Cited by 50 publications

References 37 publications

Design and implementation of a new fractional-order Hopfield neural network system

Design and implementation of a new fractional-order Hopfield neural network system

On the modeling of some triodes-based nonlinear oscillators with complex dynamics: case of the Van der Pol oscillator

Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation

Contact Info

Product

Resources

About