Torus breakdown in a two-stroke relaxation memristor Ginoux, Jean-Marc; Meucci, Riccardo; Euzzor, Stefano ...
Chaos, solitons & fractals/Chaos, solitons and fractals,
December 2021, 2021-12-00, 2021-12, Letnik:
153, Številka:
2
Journal Article
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•Two stroke oscillator.•Memristor.•Uni junction transistor.•Torus breakdown.•Relaxation and chaotic oscillators.
Experimental study of a two-stroke relaxation oscillator (TSO) has enabled to show ...that this electronic component has the same features as the so-called “memristor”. So, we have used the memristor’s direct current (DC) vM−iM characteristic for modeling the TSO’s DC current-voltage characteristic. This led us to confirm on one hand, that the TSO is a memristor and, on the other hand to propose a new four-dimensional autonomous dynamical system allowing to describe experimentally observed phenomena such as the transition from a limit cycle to torus breakdown.
Abstract
In 1976, Leon Chua showed that a thermistor can be modeled as a memristive device. Starting from this statement we designed a circuit that has four circuit elements: a linear passive ...inductor, a linear passive capacitor, a nonlinear resistor and a thermistor, that is, a nonlinear “locally active” memristor. Thus, the purpose of this work was to use a physical memristor, the thermistor, in a Muthuswamy–Chua chaotic system (circuit) instead of memristor emulators. Such circuit has been modeled by a new three-dimensional autonomous dynamical system exhibiting very particular properties such as the transition from torus breakdown to chaos. Then, mathematical analysis and detailed numerical investigations have enabled to establish that such a transition corresponds to the so-called route to Shilnikov spiral chaos but gives rise to a “double spiral attractor”.
Ischemic damage to the brain triggers substantial reorganization of spared areas and pathways, which is associated with limited, spontaneous restoration of function. A better understanding of this ...plastic remodeling is crucial to develop more effective strategies for stroke rehabilitation. In this review article, we discuss advances in the comprehension of post-stroke network reorganization in patients and animal models. We first focus on rodent studies that have shed light on the mechanisms underlying neuronal remodeling in the perilesional area and contralesional hemisphere after motor cortex infarcts. Analysis of electrophysiological data has demonstrated brain-wide alterations in functional connectivity in both hemispheres, well beyond the infarcted area. We then illustrate the potential use of non-invasive brain stimulation (NIBS) techniques to boost recovery. We finally discuss rehabilitative protocols based on robotic devices as a tool to promote endogenous plasticity and functional restoration.
•The dynamics of nonlinear excitations in DNA is studied.•In the model the bases of DNA are subject to small longitudinal displacements.•A coupling between twisting and rising of bases is introduced ...in the model.•It is shown that localized travelling wave solutions of the longitudinal field exist.
A model of the DNA is proposed and studied analytically and numerically. The model is an extension of a well known model and describes the double helix as two chains of pendula (each pendulum representing a base). Each base (or pendulum) can rotate and translate along the helix axis. In the continuum limit the system is described by the perturbed Sine–Gordon equation describing the twist of the bases and by a nonlinear partial differential equation (PDE) describing the longitudinal displacements of the bases. This coupled system of PDEs was studied analytically using different approaches and the corresponding results were tested through numerical simulations. It was found that if the coupling parameters satisfy a well defined relationship, then there exist bounded travelling wave solutions.
In this paper, a biophysical neural network model consisting of a pyramidal neuron, an interneuron, and the astrocyte is studied. The corresponding dynamical properties are mainly investigated by ...using numerical simulations. The results show that the presence of the adenosine triphosphate and of the interneuron impacts the overall neural activity. It is shown that the fluxes of calcium through the cellular membrane strongly affect the modulation of the neural activity arising from the astrocyte.
Limited restoration of function is known to occur spontaneously after an ischemic injury to the primary motor cortex. Evidence suggests that Pre-Motor Areas (PMAs) may "take over" control of the ...disrupted functions. However, little is known about functional reorganizations in PMAs. Forelimb movements in mice can be driven by two cortical regions, Caudal and Rostral Forelimb Areas (CFA and RFA), generally accepted as primary motor and pre-motor cortex, respectively. Here, we examined longitudinal changes in functional coupling between the two RFAs following unilateral photothrombotic stroke in CFA (mm from Bregma: +0.5 anterior, +1.25 lateral).
Local field potentials (LFPs) were recorded from the RFAs of both hemispheres in freely moving injured and naïve mice. Neural signals were acquired at 9, 16 and 23 days after surgery (sub-acute period in stroke animals) through one bipolar electrode per hemisphere placed in the center of RFA, with a ground screw over the occipital bone. LFPs were pre-processed through an efficient method of artifact removal and analysed through: spectral,cross-correlation, mutual information and Granger causality analysis.
Spectral analysis demonstrated an early decrease (day 9) in the alpha band power in both the RFAs. In the late sub-acute period (days 16 and 23), inter-hemispheric functional coupling was reduced in ischemic animals, as shown by a decrease in the cross-correlation and mutual information measures. Within the gamma and delta bands, correlation measures were already reduced at day 9. Granger analysis, used as a measure of the symmetry of the inter-hemispheric causal connectivity, showed a less balanced activity in the two RFAs after stroke, with more frequent oscillations of hemispheric dominance.
These results indicate robust electrophysiological changes in PMAs after stroke. Specifically, we found alterations in transcallosal connectivity, with reduced inter-hemispheric functional coupling and a fluctuating dominance pattern. These reorganizations may underlie vicariation of lost functions following stroke.
Environmental enrichment (EE) is an experimental protocol based on a complex sensorimotor stimulation that dramatically affects brain development. While it is widely believed that the effects of EE ...result from the unique combination of different sensory and motor stimuli, it is not known whether and how cortico-cortical interactions are shaped by EE. Since the primary visual cortex (V1) is one of the best characterized targets of EE, we looked for direct cortico-cortical projections impinging on V1, and we identified a direct monosynaptic connection between motor cortex and V1 in the mouse brain. To measure the interactions between these areas under standard and EE rearing conditions, we used simultaneous recordings of local field potentials (LFPs) in awake, freely moving animals. LFP signals were analyzed by using different methods of linear and nonlinear analysis of time series (cross-correlation, mutual information, phase synchronization). We found that EE decreases the level of coupling between the electrical activities of the two cortical regions with respect to the control group. From a functional point of view, our results indicate, for the first time, that an enhanced sensorimotor experience impacts on the brain by affecting the functional crosstalk between different cortical areas.
We propose a new two dimensional model for the UJT (Unipolar Junction Transistor) relaxation oscillator whose parameters were chosen by fitting the experimental data. The dynamical properties of the ...model were studied by using nonlinear dynamics methods and it was proved that self-sustained oscillations may occur. Then, the system was forced to study the transition to chaos, reproducing the torus breakdown mechanism observed experimentally. Finally, two identical systems were diffusively coupled and the synchronization properties have been studied.
•New model for the UJT relaxation oscillator.•Dynamical characterization of oscillating behaviour.•Transition to chaos via quasi-periodicity (torus breakdown).•Synchronization characterization.
Brain aging is characterized by global changes which are thought to underlie age-related cognitive decline. These include variations in brain activity and the progressive increase in the ...concentration of soluble amyloid-β (Aβ) oligomers, directly impairing synaptic function and plasticity even in the absence of any neurodegenerative disorder. Considering the high social impact of the decline in brain performance associated to aging, there is an urgent need to better understand how it can be prevented or contrasted. Lifestyle components, such as social interaction, motor exercise and cognitive activity, are thought to modulate brain physiology and its susceptibility to age-related pathologies. However, the precise functional and molecular factors that respond to environmental stimuli and might mediate their protective action again pathological aging still need to be clearly identified. To address this issue, we exploited environmental enrichment (EE), a reliable model for studying the effect of experience on the brain based on the enhancement of cognitive, social and motor experience, in aged wild-type mice. We analyzed the functional consequences of EE on aged brain physiology by performing in vivo local field potential (LFP) recordings with chronic implants. In addition, we also investigated changes induced by EE on molecular markers of neural plasticity and on the levels of soluble Aβ oligomers. We report that EE induced profound changes in the activity of the primary visual and auditory cortices and in their functional interaction. At the molecular level, EE enhanced plasticity by an upward shift of the cortical excitation/inhibition balance. In addition, EE reduced brain Aβ oligomers and increased synthesis of the Aβ-degrading enzyme neprilysin. Our findings strengthen the potential of EE procedures as a non-invasive paradigm for counteracting brain aging processes.
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