Complex dynamics and autapse-modulated information patterns in memristive Wilson neurons

Njitacke, Zeric Tabekoueng; Takembo, Clovis Ntahkie; Koumetio, Bernard Nzoko; Awrejcewicz, Jan

doi:10.1007/s11071-022-07738-3

Cited by 10 publications

(2 citation statements)

References 27 publications

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“…Hence the use of equation (5) permits us to examine the stability of the fifteen fixed points obtained previously for particular rangs of parameters, the results are recorded in table 1. Then, it is observed that the system undergoes the phenomenon of Hopf bifurcation [42] which is going to be shown analytically in the next part.…”

Section: Equilibria and Stabilitymentioning

confidence: 96%

A circulant inertia three Hopfield neuron system: dynamics, offset boosting, multistability and simple microcontroller- based practical implementation

Balaraman,

Nzoulewa Dountsop,

Kengne

et al. 2023

Phys. Scr.

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This work investigates the dynamics and implementation of a three inertia circulant neurons model with each neuron activated by a non-monotonic Crespi function. Owing its source to the work previously done by Z. Song and co-authors[1], we proposes a network made up of three neurons connected cyclically. Z. Song and collaborators studied the dynamics of an inertia neural system and demonstrated the mixed coexistence of periodic orbits and chaotic attractors but they show the coexistence of only two and four attractors. Recently, B.F.Boya and co-workers[2] break the symmetry of the previous system then, demonstrated the coexistence of two, three, four and six attractors. Here, is analyzed a model capable of the coexisting of two, three, four, six, eight and ten attractors basing on different starting points. Analytically, the system is dissipative and presents fifteen equilibrium unstable for a given rank of parameters. This is the reason of the demonstration of Hopf bifurcation in the model when the bifurcation parameter is the first synaptic weight. Also, using bifurcation diagrams, Maximum Lyapunov Exponent diagram, phase portraits, two parameters Lyapunov diagrams, double-side Poincaré section and basin of attraction, intriguing phenomena have been demonstrated such as hysteresis, coexistence of parallel branches of bifurcation, antimonotonicity to name these few. Moreover, offset boosting is exhibiting associated once with transient oscillation leading from one chaotic state to another which is an input to the dynamics of inertia neural systems particularly and chaotic system in general. A number of coexisting attractors have been developed by the new network which can be used to build sophisticated cryptosystem or to explain the possible tasks of a brain in normal or abnormal cases. In other to emphasize the feasibility of the model, a microcontroller-based implementation has been applied to demonstrate the period-doubling route to chaos obtained numerically.

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Section: Equilibria and Stabilitymentioning

confidence: 96%

A circulant inertia three Hopfield neuron system: dynamics, offset boosting, multistability and simple microcontroller- based practical implementation

Balaraman,

Nzoulewa Dountsop,

Kengne

et al. 2023

Phys. Scr.

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show abstract

“…Since the aforementioned works are all related to dynamical systems, one striking and widespread phenomenon found in those systems is the coexistence of patterns (multistability). Multistability in a model is characterized by the presence of multiple stable states, which can be achieved by modifying the initial conditions while keeping the parameters constant [27,28]. Despite the large number of works already addressed on the calcium oscillation model [23][24][25][26], there is currently no study that specifically focuses on analyzing the coexisting bifurcations with more than two oscillating states in such model.…”

Section: Introductionmentioning

confidence: 99%

Global and multistable dynamics in calcium oscillations model

Subramanian,

Tabekoueng Njitacke,

Awrejcewicz

et al. 2023

Phys. Scr.

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In most animal and plant cells, the information’s processing is insured by calcium ions. This contribution studies the global dynamics of a model of calcium oscillation. From the stability analysis, it is found that the oscillations of that model are self-excited since they are generated from unstable equilibria. Using two-parameter charts, the general behavior of the model is explored. From the hysteresis analysis using bifurcation diagrams with their related Largest Lyapunov Exponent (LLE) graphs, the coexisting oscillation modes are recorded. This phenomenon is characterized by the simultaneous existence of periodic and chaotic oscillations in the considered model by just varying the initial conditions. Using a set of parameters for which the model exhibits multistability, the basins of attraction related to each coexisting solution are computed and enable the capture of any coexisting pattern.

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Nonlinear mechanisms for opposite responses of bursting activities induced by inhibitory autapse with fast and slow time scale

Yang

et al. 2023

Nonlinear Dyn

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Complex dynamics and autapse-modulated information patterns in memristive Wilson neurons

Cited by 10 publications

References 27 publications

A circulant inertia three Hopfield neuron system: dynamics, offset boosting, multistability and simple microcontroller- based practical implementation

A circulant inertia three Hopfield neuron system: dynamics, offset boosting, multistability and simple microcontroller- based practical implementation

Global and multistable dynamics in calcium oscillations model

Nonlinear mechanisms for opposite responses of bursting activities induced by inhibitory autapse with fast and slow time scale

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