Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization a heterogeneous small-world chaotic Hindmarsh–Rose network. The effects various network parameters on behaviour are discussed with some biological explanations. Complete networks studied theoretically by master stability function method. It shown that coupling strength necessary or decreases neuron number, node degree...

More evidence indicates that central nervous system diseases are related to abnormal regulation of the reciprocal expression nerve cells and astrocytes. In this paper, we investigated dynamics a model incorporating both neuron an astrocyte elucidate effective interaction between two components. coupled system, external stimulation is applied astrocyte, respectively. The results showed after successive stimuli separated by 20 s, neurons astrocytes can exhibit so-called hyperexcitability...

Oscillatory patterns in a one-pool model with Ca 2+ -activated IP 3 degradation are presented and classified, based on fast/slow dynamical analysis two-parameter bifurcations. The whole parameter space can be partitioned into two parts, that is, the oscillatory rest regions. For this purpose, we perform continuation of fold bifurcation, Hopf bifurcation saddle-node limit cycles, respectively. Several distinct topological types complex intracellular oscillations (especially bursting)...

A mathematical model proposed by Grubelnk et al. [Biophys. Chew,. 94 (2001) 59] is employed to study the physiological role of mitochondria and cytosolic proteins in generating complex Ca2+ oscillations. Intracel-lular bursting calcium oscillations point–point, point–cycle two-folded limit cycle types are observed explanations given based on fast/slow dynamical analysis, especially for types, which have not been reported before. Furthermore, synchronization coupled bursters via gap junctions...

Based on the fast–slow dynamics and bifurcation analysis, two different types of bursting, that is, “subHopf/homoclinic” “circle/fold cycle” are presented analyzed in a two-compartment neuron model with current feedback control due to totally generation mechanisms. The synchronization transition process from burst nearly complete is considered electrically coupled nonidentical neurons, analysis can be extended explore bursting behavior synchronization. multitime-scale may help us better...

In this paper, the chaotic behavior as well synchronization of fractional-order Chua's system is studied. By using lyapunov exponent analysis, we find that minimal fractional order to generate 0.880. Chaos also investigated based on active control. Finally, effectiveness proposed method confirmed by numerical simulations.

The contribution of this present paper is to propose a method that combines chemical Brusselator reaction‐diffusion system with biological cell via gap junction for controlling and visualizing the frequency magnitude chaotic intracellular calcium oscillations in two types, including nonexcitable cells glial cells. This produces wide variety oscillatory behaviors similar those reported numerous experiments. We particularly show majority chaos cases, reactor coupling can induce generation...

This study investigated the stability and bifurcation of a nonlinear system model developed by Marhl et al. based on total Ca2+ concentration among three different stores. In this study, qualitative theories center manifold were used to analyze equilibria. The parameter drove undergo two supercritical bifurcations. It was hypothesized that appearance disappearance oscillations are driven them. At same time, saddle-node torus also found in process exploring bifurcation. Finally, numerical...

Some new elements are introduced into a mathematical model of intracellular calcium oscillations, which make it particularly suitable for the study bifurcation. In addition to generating regular such modified can be used reproduce burst discharges similar those recorded in experiments and describe two types oscillatory phenomena. By means fast/slow dynamical analysis, we explore bifurcation transition mechanisms associated with bursters due changes interaction slow variables different timescales.

New symmetric property, composed of equivariant condition, was generated near each bifurcation point in numerical simulation Brusslator reaction diffusion model. It found that when the condition is added to Brusselator model, results can exhibit symmetry phenomena. Different subgroups were verified be cause generation this breaking property. This manifests existence nontrivial solution model.Furthermore, it shown parameter increased, different branches bifurcating from steady also appears...

Considering four coupled identical and non-identical bursters with different topological types, both of the synchronization transition paths influence oscillatory patterns on are studied. Our results reveal that phenomena multi-time scale, phase-locking, chaos anti-phase transitions can be separately found in systems by varying coupling strength. The above analysis could provide us a further clue for better understanding mechanism intracellular Ca2+ signaling.

This paper proposes a new fuzzy sliding mode control scheme for uncertain two-degree of freedom polar robot system. Based on the proposed scheme, stability closed-loop system is established. The designed controller can drive to desired state. corresponding numerical simulations are demonstrated verify effectiveness method.

Pre-Bötzinger complex is considered to have a closely relationship with the respiratory rhythms. In this paper, we investigate bursting phenomena of pre-Bötzinger neuron periodic slow stimulation. Since external forcing visit spiking and rest areas in different ways, thus system could generate various patterns. With taken as variable that modulates dynamics system, types are distinguished generation mechanism explored by using combination two parameter bifurcation analysis fast...

In this paper, a model proposed by Marhl et al. is considered to investigate the effect of several parameters on calcium bursting oscillation behavior.Different types are presented.Fast-slow burster analysis and first return map used explain mechanism four bursting.The results instructive for understanding role these played in complex dynamics Marhl-Haberichter model.

The release of ink in Aplysia californica occurs selectivelyto long-lasting stimuli. There is a good correspondence betweenfeatures the behavior and firing pattern gland motorneurons. Indeed, neurons do not fire for brief inputs thereis delayed long duration inputs. biophysical mechanisms longdelay before due to transient potassium current whichactivates rapidly but inactivates more slowly. Based onvoltage-clamp experiments, nine-variable Hodgkin-Huxley-like model inkgland motor was...

<abstract><p>The central nervous system extensively expresses Ca<sup>2+</sup>-stimulated K<sup>+</sup> channels, which serve to use Ca<sup>2+</sup> control their opening and closing. In this study, we explore the numerical computation of Hopf bifurcation in Chay model based on equilibrium point's stability center manifold theorem illustrate emergence complicated neuronal bursting induced by variation conductance...

<abstract> <p>In this work, we focus on a nonlinear dynamical model proposed by Lavrentovich et al. to compute and simulate spontaneous Ca<sup>2+</sup> oscillations evoked calcium ion efflux in astrocytes. Selected parameters are chosen, with observation of periodic chaotic cytosol. The stability analysis equilibrium is conducted using the center manifold theorem investigate dynamics underlying results indicate that Hopf bifurcation represents changes oscillations. In...

This paper discusses a problem of the Hopf bifurcation control for mathematical model intracellular calcium oscillations by calculating curvature coefficient limit cycle and theory.We find that appearance disappearance in this system are due to supercritical subcritical equilibrium points, respectively.In addition, nonlinear feedback controller is proposed frequency amplitude periodic orbits arising from bifurcation.Numerical analysis simulation results carried out illustrate validity...

This paper addresses the synchronization problem of a class uncertain chaotic systems with triangular structure based on adaptive high-gain observer. The states master system are not available for feedback. Based Lyapunov stability criterion, an observer is designed to estimate system. Fuzzy logic used unknown nonlinear functions online, and fuzzy constructed. backstepping approach, controller recursively. Finally simulation studies given confirm our method.