The effects of symmetry breaking on the dynamics of an inertial neural system with a non-monotonic activation function: Theoretical study, asymmetric multistability and experimental investigation

Boya, Bertrand Frederick Boui A; Ramakrishnan, Balamurali; Effa, Joseph Yves; Kengne, Jacques; Rajagopal, Karthikeyan

doi:10.1016/j.physa.2022.127458

Cited by 8 publications

(7 citation statements)

References 30 publications

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“…Bursting oscillation, is a most complex non-linear phenomenon of alternation between rest and peak states. This interesting phenomenon has been discovered in many non-linear systems [39][40][41] and describe activity of brain.…”

Section: Bursting Oscillationsmentioning

confidence: 86%

Dynamics effects of bias current composed on inertial neural system: multistability control and application in image encryption

et al. 2023

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The function of the biological nervous system is related to its dynamics. This paper explored the dynamics effects of bias current composed on inertial neural system based with two neurons. The model affected by the bias current can induce a reduction in the number of equilibrium points, the number of coexistence attractors, as well as the disturbance of the symmetry of this model compared to the model in without bias current. In absence of bias current we report multistability of up to six different attractors, symmetry birth of chaos via period-bubbling cascades in are reported in the model. Coexistence of symmetry bursting oscillations, parallel branch, and hysteresis dynamic are also presented in the system. The presence of bias current control the symmetry of the model and generates complex phenomena among others, coexistence of five asymmetric attractors, coexistence of asymmetric bubble and asymmetric bursting oscillation. Equilibrium point and Hopf bifurcation are perform in the paper. Furthermore, control of multistability is used for future application in engineering. Security analyses indicates that the proposed image encryption scheme exhibits a good encryption performance and can withstand known attacks.

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Section: Bursting Oscillationsmentioning

confidence: 86%

Dynamics effects of bias current composed on inertial neural system: multistability control and application in image encryption

et al. 2023

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“…antimonotonicity). These types of oscillations have been experienced by many neuronal networks [15,23]. For the set of parameters as in the caption of figure 7, Fiegenbaum trees (bubbles) are obtained using the bifurcation diagrams of the variable u with respect of the first synaptic weight c1 .…”

Section: Antimonotonicity and Offset Boostingmentioning

confidence: 99%

“…With the use of Crespi function as activation function in 2019, the delayed inertial network disclosed the coexistence of two symmetric periodic orbits, multistability of periodic orbits and multistability of chaotic attractors. Recently, Boya and collaborators [15] break the symmetry of the previous system by introducing a constant b into the non-monotonic activation function. With the help of analytical, numerical and practical implementation with a microcontroller-based system, several relevant phenomena were uncovered such as transient bifurcation, bursting oscillation, amplitude control; offset boosting, antimonotonicity then, the coexistence of two, three, four and six attractors to name few.…”

Section: Introductionmentioning

confidence: 99%

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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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“…In computational neuroscience, therefore, several research studies have been carried out to improve our knowledge to the electrical activity of coupled neurons models [3] [3][4][5]. As a result, several phenomena were observed in those works, including firing activity [6,7], multi-scroll dynamics [8][9][10], and multistability [11][12][13]. The design of simple chaotic models with complex chaotic orbits and multiple coexistence of attractors is still a hot topic in nonlinear dynamics area [14,15].…”

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.

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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.

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The effects of symmetry breaking on the dynamics of an inertial neural system with a non-monotonic activation function: Theoretical study, asymmetric multistability and experimental investigation

Cited by 8 publications

References 30 publications

Dynamics effects of bias current composed on inertial neural system: multistability control and application in image encryption

Dynamics effects of bias current composed on inertial neural system: multistability control and application in image encryption

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

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

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