Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons.
نویسندگان
چکیده
We study a plethora of chaotic phenomena in the Hindmarsh-Rose neuron model with the use of several computational techniques including the bifurcation parameter continuation, spike-quantification, and evaluation of Lyapunov exponents in bi-parameter diagrams. Such an aggregated approach allows for detecting regions of simple and chaotic dynamics, and demarcating borderlines-exact bifurcation curves. We demonstrate how the organizing centers-points corresponding to codimension-two homoclinic bifurcations-along with fold and period-doubling bifurcation curves structure the biparametric plane, thus forming macro-chaotic regions of onion bulb shapes and revealing spike-adding cascades that generate micro-chaotic structures due to the hysteresis.
منابع مشابه
On the dynamics of chaotic spiking-bursting transition in the Hindmarsh-Rose neuron.
The paper considers the neuron model of Hindmarsh-Rose and studies in detail the system dynamics which controls the transition between the spiking and bursting regimes. In particular, such a passage occurs in a chaotic region and different explanations have been given in the literature to represent the process, generally based on a slow-fast decomposition of the neuron model. This paper propose...
متن کاملGenesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle
We present two hypotheses on the mathematical mechanism underlying bursting dynamics in a class of differential systems: (1) that the transition from continuous firing of spikes to bursting is caused by a crisis which destabilizes a chaotic state of continuous spiking; and (2) that the bursting corresponds to a homoclinicity to this unstable chaotic state. These propositions are supported by a ...
متن کاملClusters of synchronization and bistability in lattices of chaotic neurons
– We investigated different regimes of synchronization in large lattices of chaotic spiking-bursting neurons. The lattices exhibit the following features: developed spatio-temporal disorder with no synchronization; spatial clusters of bursting synchronization; homogeneous bursting synchronization; and complete chaotic synchronization. We observed a bistable synchronization phenomenon in a wide ...
متن کاملStrange Nonchaotic Bursting in A Quasiperiodially-Forced Hindmarsh-Rose Neuron
We study the transition from a silent state to a bursting state by varying the dc stimulus in the Hindmarsh-Rose neuron under quasiperiodic stimulation. For this quasiperiodically forced case, a new type of strange nonchaotic (SN) bursting state is found to occur between the silent state and the chaotic bursting state. This is in contrast to the periodically forced case where the silent state t...
متن کاملTime-delay effect on the bursting of the synchronized state of coupled Hindmarsh-Rose neurons.
The time-delay effect on the bursting of the synchronized state of coupled Hindmarsh-Rose neurons is investigated in this paper. The time-delay influence on the structure of the slow manifold is first studied by using the method of stability switch. And then on the basis of the geometric singular perturbation theory, case studies are given to show that the time delay can suppress the bursting o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Chaos
دوره 24 2 شماره
صفحات -
تاریخ انتشار 2014