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Memristor coupled neuronal networks can simulate the complex interactions between neurons in biological neuronal networks. These capture the current and synaptic transmission between neurons through mathematical equations, thus reflecting the signal transmission and integration in biological neuronal networks. This paper presents a five-dimensional isomorphic memristor coupled adaptive synaptic neuron (mCASN) network using a non-ideal memristor to couple two-dimensional adaptive synaptic neurons. The theoretical analysis of equilibrium points shows that the mCASN network has many different stability types. The complex parameters-dependent bifurcation behaviors are studied using various numerical methods, and the initial state-dependent coexistence behaviors and the riddled-like basins of attraction sensitive to initial states are further revealed, which proves that the coupled network has multistability. In addition, using the normalized average synchronization error method, we reveal that the mCASN network has synchronization characteristics controlled by parameters and initial states. The complete synchronization and lag synchronization induced by the network parameters, the internal variable of the coupled memristor, and the state variable of the sub-neuron are numerically analyzed. Finally, the mCASN network is implemented using an MCU-based digital hardware platform, and the numerical results are verified. • A 5-D isomorphic mCASN network by memristor coupled two identical 2-D neurons is proposed. • The parameters-dependent bifurcation behaviors and initial states-dependent coexistence behaviors are studied. • Complete synchronization and lay synchronization state involving parameters and initial states are investigated. • The mCASN network is implemented by using a digital development platform to verify numerical results. [ABSTRACT FROM AUTHOR]

As a connecting synapse, memristor is considered as a feasible device for representing the magnetic induction between two coupled neurons to enable the information exchange. However, the effect of memristor as a coupling synapse between two map-based neurons on synchronous activity has not received sufficient attention. To this end, an extensible locally active memristor is proposed, and its various characteristics are demonstrated by several existing methods. Based on the proposed memristor and two map-based neurons, a memristor synapse-coupled neuron model is constructed to investigate the memristor-induced synchronous firing activities. Taking the coupling strength and memristor synapse initial state as controllable variables, several analysis methods, such as phase diagram, normalized mean synchronization error, similarity function, and phase difference, are used to clearly reveal various synchronization phenomena triggered by the introduced memristor, including complete synchronization, lag synchronization, and phase synchronization, as well as the accompanying spiking/bursting firing behaviors. In particular, the generation and transition of synchronization depend on the initial states of the memristor synapse-coupled neuron model, resulting in the coexistence of firing modes. The correctness of these synchronous firing activities is validated by digital hardware experiments. Numerical and hardware results show that the memristor, as a coupling synapse, provides a flexible and reliable control scheme for the synchronization between neurons. • An extensible locally active memristor is presented and its characteristics are demonstrated. • A memristor synapse-coupled neuron model is constructed based on two map-based neurons. • The memristor-induced synchronous firing activities are revealed by several analysis methods. • Digital hardware experiments validate the correctness of these synchronous firing activities. [ABSTRACT FROM AUTHOR]

The complexity of memristive chaotic systems determines whether it is suitable for applications in different subjects. To enhance complexity both in performance and diversity, this article first proposes a discrete model of locally active memristor (LAM) and conceives a three-dimensional memristive multi-cavity map by coupling LAM with the existing sine and cosine modulation (SCM) map. This map is named LAM-SCM map and has numerous independent fixed points with different stabilities. Numerical simulations reveal the memristive parameters-relied lossless displacement and self-shift of multi-cavity attractors, indicating the dynamical effects of LAM on the existing SCM map. The initial-relied dynamics distributions are disclosed by grid basins of attraction, showing the emergence of initial-boosting coexistence. Besides, the performance comparisons verify the superiority of LAM-SCM map over the existing SCM map. Finally, a hardware platform has been developed on FPGA to implement the LAM-SCM map and the captured attractors validate the numerical results. On this basis, we devise a 32-bit pseudorandom number generator (PRNG) based on chaos and implement it on the FPGA-based hardware platform to obtain high-speed and reconfigurable pseudorandom numbers. The results show that the proposed map has enhanced chaos complexity and rich dynamics diversity, which ensures the availability of hardware PRNG. • A locally active memristor-based sine and cosine modulation multi-cavity map is presented. • Multi-cavity attractors and grid basins of attraction are investigated by numerical simulations. • Performance tests and comparisons are conducted to show that the map has high randomness. • A chaos-based 32-bit pseudorandom number generator is designed and implemented on FPGA. [ABSTRACT FROM AUTHOR]

Due to more complex behavior and larger number of control parameters, high-dimensional chaotic map generation methods may provide more satisfactory performance in various practical applications compared to low-dimensional counterparts. Designing n -dimensional (n D) chaotic map generation methods for generating chaotic maps in arbitrary dimensions with desired dynamics is an interesting but challenging task. In this paper, we propose a universal framework called the n D circularly shifting chaotic map generation method (n D-CS), which utilizes existing one-dimensional chaotic maps as seed maps to generate n D chaotic maps with complex and robust behaviors. Theoretical analysis proves that when specific criteria are met by its control parameters, our n D-CS can exhibit complex and robust hyperchaotic behavior in the sense of Lyapunov exponent. To demonstrate the effectiveness of our n D-CS, we first employ it to generate three examples of three-dimensional hyperchaotic maps. The results indicate high-performance indicators of these new chaotic maps. Furthermore, we compare the n D chaotic maps generated by our n D-CS to those produced by existing methods. The results demonstrate that our chaotic maps have a better overall performance. [ABSTRACT FROM AUTHOR]

To characterize neuronal firing activities and elucidate its bifurcation mechanisms, a memristor-based FitzHugh-Nagumo (FHN) circuit is designed based on the FHN circuit architecture combined with a first-order memristive simulator, and its normalized system with periodic and quasi-periodic bursting oscillations is established. With the change of externally applied excitation, the memristor-based FHN system has the time-varying equilibrium point where the number, position and stability evolve slowly over time. In an evolution period of the time-domain waveform, different fold and/or Hopf bifurcations are triggered, resulting in periodic or quasi-periodic bursting oscillations. To explain the intrinsic bifurcation mechanisms, the fold and Hopf bifurcation sets are built and the transitions between the resting and spiking states are demonstrated, thus identifying the Hopf/fold and Hopf/Hopf bursting oscillations. Finally, based on the circuit simulation model, analog circuit simulations and hardware circuit measurements are developed for the memristor-based FHN circuit to confirm MATLAB numerical simulations. In addition, it is worth noting that the proposed circuit is a simple non-autonomous memristive neuron circuit that is particularly easy to physically implement. • A memristor-based FitzHugh-Nagumo circuit with periodic/quasi-periodic bursting oscillations is designed. • The time-varying equilibrium points with stability evolutions for some parameter settings are analyzed. • Bifurcations to periodic and quasi-periodic bursting oscillations are theoretically demonstrated. • Analog circuit simulations and hardware circuit measurements are developed for the proposed circuit. [ABSTRACT FROM AUTHOR]

The diversity of firing patterns and their bifurcation mechanisms of a neuron circuit are crucial for exploiting bionic applications. This paper constructs an N-type locally active memristor (LAM)-based FitzHugh–Nagumo (FHN) circuit by replacing the tunnel-diode in the original FHN circuit. Numerical simulations and hardware measurements reveal that the N-type LAM-based FHN circuit can reproduce rich neuromorphic firing patterns of quasi-periodic/periodic bursting behaviors and chaotic/periodic spiking behaviors. The bursting and spiking behaviors are triggered by a low-frequency stimulus and a high-frequency one, respectively. Besides, the fold and Hopf bifurcation sets are depicted. Then, the bifurcation mechanisms for the quasi-periodic and periodic bursting behaviors via Hopf/Hopf and Hopf/fold bifurcations are theoretically deduced by time-domain waveform and equilibrium trajectory. The numerical results and hardware experiments exhibit the effectiveness of the proposed memristive FHN circuit in reproducing abundant firing patterns of bursting and spiking behaviors. • An N-type locally active memristor-based FHN circuit is first built by replace the tunnel-diode. • Fast–slow dynamics versus to high-frequency and low-frequency stimuli are explored. • Bifurcation mechanisms for quasi-periodic and periodic bursting behaviors are deduced. • Hardware experiments are executed to validate the generation of spiking and bursting behaviors. [ABSTRACT FROM AUTHOR]

Eleven years have passed since the discovery of the first chaotic hidden attractor in Chua system with piecewise-linear nonlinearity. Experimental observation of such attractor is still a hard work as the attraction basin of such hidden attractor does not intersect with any system equilibrium point and is far away from the origin. The key technical difficulty is the accurate configuration of non-zero initial values for dynamic elements. In this Letter, offset control is applied to shift the attraction basin and mapping the non-zero initial values to zero ones. Consequently, the attraction basin is intersect with origin, which allows us to experimentally observe such hidden attractor via pre-discharge all dynamic elements. • Graphical structure of attraction basin of hidden Chua's attractor is investigated. • Offset control is applied for effective observation of hidden attractor in experiment. • The observating strategy of hidden oscillations can be extended to high-dimensional nonlinear systems. [ABSTRACT FROM AUTHOR]