Memristive effects on an improved discrete Rulkov neuron model

Bao, Han; Li, KeXin; Ma, Jun; Hua, ZhongYun; Xu, Quan; Bao, BoCheng

doi:10.1007/s11431-023-2432-1

Cited by 32 publications

(3 citation statements)

References 44 publications

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“…Bao et al [31] designed a parallel bi-memristor hyperchaotic map. The discrete memristive Rulkov neuron map [32,33] was developed by introducing a DM into a Rulkov neuron model. A fractional memristive map is proposed in [34].…”

Section: Introductionmentioning

confidence: 99%

An adaptive energy regulation in a memristive map linearized from a circuit with two memristive channels

Yang,

Zhou,

2024

Commun. Theor. Phys.

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The nonlinear circuits can show multistability when magnetic flux-dependent memristor (MFDM) or charge-sensitive memristor (CSM) is incorporated into one branch circuit, which is helpful for estimating magnetic or electric field effects. In this paper, two different kinds of memristors are incorporated into two branch circuits composed of a capacitor and a nonlinear resistor, thus a memristive circuit with double memristive channels is designed. The circuit equations are presented, and the dynamics in this oscillator with two memristive terms are discussed. Then the memristive oscillator is converted into a memristive map by applying linear transformation on the sampled time series for memristive oscillator. The Hamilton energy function for the memristive oscillator is obtained by using the Helmholtz theorem, and it can be mapped from the field energy of the memristive circuit. An energy function for the dual memristive map is suggested by imposing suitable weights on the discrete energy function. The dynamical behaviors of the new memristive map are investigated, and an adaptive law is proposed to regulate the firing mode in the memristive map. This work will provide theoretical basis and experimental guidance for oscillator-to-map transformation and discrete map energy calculation.

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Section: Introductionmentioning

confidence: 99%

An adaptive energy regulation in a memristive map linearized from a circuit with two memristive channels

Yang,

Zhou,

2024

Commun. Theor. Phys.

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“…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.

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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.

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“…One of the primary approaches for constructing chaotic maps is mathematical models, such as cylindrical [8], spherical cavities [9], and cycloid models [10]. Another is to strengthen the chaotic strategies, such as coupling [11,12], cascading [13,14], synchronization [15,16], these methods can be flexibly applied to existing chaotic maps [17] or nonlinear equations [18], or using memristors [19][20][21], neural networks [22,23], filters [24] to further enhance chaotic behaviors.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of multicavity hyperchaotic maps with rotational control operation and its applications

Zhu,

Sun,

et al. 2024

Phys. Scr.

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To provide more complex and random chaotic maps to applications and algorithms, we propose a boundary coupled modulation (BCM) model. By introducing the rotation-matrix (ROT), the corresponding rotation boundary coupled modulation (RBCM) model are constructed, and a series of hyperchaotic maps are generated with various attractors and numerous fixed points. The shape and size of the multicavity can be adjusted by controlling the parameters. Interestingly, RBCM maps are controlled by changing rotation coefficients (Rot-C, d, e, and θ), which can rotate the attractor of the enhanced BCM at any angle and direction. RBCM maps produce a more uniform topological space, and have multiple pairs of symmetric coexisting attractors. The BCM and RBCM maps exhibit rich dynamical behaviors, high complexity, and strong randomness.To verify the engineering practicability, we apply the BCM and RBCM maps to design pseudo-random number generators (PRNG), and test it with NIST, quadrature amplitude modulation (QAM) system. Finally, the FPGA implementation of the proposed chaotic map verifies.

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Memristive effects on an improved discrete Rulkov neuron model

Cited by 32 publications

References 44 publications

An adaptive energy regulation in a memristive map linearized from a circuit with two memristive channels

An adaptive energy regulation in a memristive map linearized from a circuit with two memristive channels

Applying exponential unit for breaking symmetry of memristive maps

Dynamics of multicavity hyperchaotic maps with rotational control operation and its applications

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