This paper describes a novel 4-D hyperchaotic system with a high level of complexity. It can produce chaotic, hyperchaotic, periodic, and quasi-periodic behaviors by adjusting its parameters. The study showed that the new system experienced the famous dynamical property of multistability. It can exhibit different coexisting attractors for the same parameter values. Furthermore, by using Lyapunov exponents, bifurcation diagram, equilibrium points\' stability, dissipativity, and phase plots, the study was able to investigate the dynamical features of the proposed system. The mathematical model\'s feasibility is proved by applying the corresponding electronic circuit using Multisim software. The study also reveals an interesting and special feature of the system\'s offset boosting control. Therefore, the new 4D system is very desirable to use in Chaos-based applications due to its hyperchaotic behavior, multistability, offset boosting property, and easily implementable electronic circuit. Then, the study presents a voice encryption scheme that employs the characteristics of the proposed hyperchaotic system to encrypt a voice signal. The new encryption system is implemented on MATLAB (R2023) to simulate the research findings. Numerous tests are used to measure the efficiency of the developed encryption system against attacks, such as histogram analysis, percent residual deviation (PRD), signal-to-noise ratio (SNR), correlation coefficient (cc), key sensitivity, and NIST randomness test. The simulation findings show how effective our proposed encryption system is and how resilient it is to different cryptographic assaults.

This study focuses on the synchronization analysis of Hindmarsh-Rose neurons coupled through a common memristor (coupled mHRN). Initially, we thoroughly examine the synchronization of two mHRNs coupled via a common memristor before exploring synchronization in a network of mHRNs. The stability of the proposed model is analyzed in three cases, demonstrating the existence of a single equilibrium point whose stability is influenced by external stimuli. The stable and unstable regions are investigated using eigenvalues. Through bifurcation analysis and the determination of maximum Lyapunov exponents, we identify chaotic and hyperchaotic trajectories. Additionally, using the next-generation matrix method, we calculate the chaotic number C0, demonstrating the influence of coupling strength on the chaotic and hyperchaotic behavior of the system. The exponential stability of the synchronous mHRN is derived analytically using Lyapunov theory, and our results are verified through numerical simulations. Furthermore, we explore the impact of initial conditions and memristor synapses, as well as the coupling coefficient, on the synchronization of coupled mHRN. Finally, we investigate a network consisting of n number of mHRNs and observe various collective behaviors, including incoherent, coherent, traveling patterns, traveling wave chimeras, and imperfect chimeras, which are determined by the memristor coupling coefficient.

Weakly coupled semiconductor superlattices under DC voltage bias are nonlinear systems with many degrees of freedom whose nonlinearity is due to sequential tunneling of electrons. They may exhibit spontaneous chaos at room temperature and act as fast physical random number generator devices. Here we present a general sequential transport model with different voltage drops at quantum wells and barriers that includes noise and fluctuations due to the superlattice epitaxial growth. Excitability and oscillations of the current in superlattices with identical periods are due to nucleation and motion of charge dipole waves that form at the emitter contact when the current drops below a critical value. Insertion of wider wells increases superlattice excitability by allowing wave nucleation at the modified wells and more complex dynamics. Then hyperchaos and different types of intermittent chaos are possible on extended DC voltage ranges. Intrinsic shot and thermal noises and external noises produce minor effects on chaotic attractors. However, random disorder due to growth fluctuations may suppress any regular or chaotic current oscillations. Numerical simulations show that more than 70% of samples remain chaotic when the standard deviation of their fluctuations due to epitaxial growth is below 0.024 nm (10% of a single monolayer) whereas for 0.015 nm disorder suppresses chaos.

In this paper, the dynamical behaviors of an SEIR epidemic system governed by differential and algebraic equations with seasonal forcing in transmission rate are studied. The cases of only one varying parameter, two varying parameters and three varying parameters are considered to analyze the dynamical behaviors of the system. For the case of one varying parameter, the periodic, chaotic and hyperchaotic dynamical behaviors are investigated via the bifurcation diagrams, Lyapunov exponent spectrum diagram and Poincare section. For the cases of two and three varying parameters, a Lyapunov diagram is applied. A tracking controller is designed to eliminate the hyperchaotic dynamical behavior of the system, such that the disease gradually disappears. In particular, the stability and bifurcation of the system for the case which is the degree of seasonality β 1 = 0 are considered. Then taking isolation control, the aim of elimination of the disease can be reached. Finally, numerical simulations are given to illustrate the validity of the proposed results.

In the framework of a project on simple circuits with unexpected high degrees of freedom, we report an autonomous microwave oscillator made of a CLC linear resonator of Colpitts type and a single general purpose operational amplifier (Op-Amp). The resonator is in a parallel coupling with the Op-Amp to build the necessary feedback loop of the oscillator. Unlike the general topology of Op-Amp-based oscillators found in the literature including almost always the presence of a negative resistance to justify the nonlinear oscillatory behavior of such circuits, our zero resistor circuit exhibits chaotic and hyperchaotic signals in GHz frequency domain, as well as many other features of complex dynamic systems, including bistability. This simplest form of Colpitts oscillator is adequate to be used as didactic model for the study of complex systems at undergraduate level. Analog and experimental results are proposed.

The Wilson-Cowan equations were originally shown to produce limit cycle oscillations for a range of parameters. Others subsequently showed that two coupled Wilson-Cowan oscillators could produce chaos, especially if the oscillator coupling was from inhibitory interneurons of one oscillator to excitatory neurons of the other. Here this is extended to show that chains, grids, and sparse networks of Wilson-Cowan oscillators generate hyperchaos with linearly increasing complexity as the number of oscillators increases. As there is now evidence that humans can voluntarily generate hyperchaotic visuomotor sequences, these results are particularly relevant to the unpredictability of a range of human behaviors. These also include incipient senescence in aging, effects of concussive brain injuries, autism, and perhaps also intelligence and creativity.NEW & NOTEWORTHY This paper represents an exploration of hyperchaos in coupled Wilson-Cowan equations. Results show that hyperchaos (number of positive Lyapunov exponents) grows linearly with the number of oscillators in the array and leads to high levels of unpredictability in the neural response.

The last two decades have seen many literatures on the mathematical and computational analysis of neuronal activities resulting in many mathematical models to describe neuron. Many of those models have described the membrane potential of a neuron in terms of the leakage current and the synaptic inputs. Only recently researchers have proposed a new neuron model based on the electromagnetic induction theorem, which considers inner magnetic fluctuation and external electromagnetic radiation as a significant missing part that can participate in neural activity. While the flux coupling of the membrane is considered equivalent to a memductance function of a memristor, standard memductance model of α + 3 β ϕ 2 has been used in the literatures, but in this paper we propose a new memductance function based on discontinuous flux coupling. Various dynamical properties of the neuron model with discontinuous flux coupling are studied and interestingly the proposed model shows hyperchaotic behavior which was not identified in the literatures. Furthermore, we consider a ring network of the proposed model and investigate whether the chimera state can emerge. The chimera state relates to the state with simultaneously coherence and incoherence in oscillatory networks and has received much attention in recent years.

We consider a multidimensional extension of Thomas-Rössler systems, that was inspired by Thomas\' earlier work on biological feedback circuits, and we report on our first results that shows its ability to sustain spatio-temporal behaviour reminiscent of chimera states. The novelty here is that its underlying mechanism is based on \"chaotic walks\" discovered by Thomas during the course of his investigations on what he called Labyrinth Chaos. We briefly review the main properties of these systems and their chaotic and hyperchaotic dynamics and discuss the simplest way of coupling, necessary for this spatio-temporal behaviour that allows the emergence of complex dynamical behaviours. We also recall Thomas\' memorable influence and interaction with the authors as we dedicate this work to his memory.