Return Map Quantization from an Integrate-and-Fire Model with Two Periodic Inputs
نویسندگان
چکیده
In this paper, we consider the Integrate-andFire Model (ab. IFM) with two periodic inputs. The IFM outputs a pulse-train which is governed by a one dimensional return map. Using the return map, the relationship between the inputs and the output is clarified: the first input determines the global shape of the return map and the IFM outputs various periodic and chaotic pulse-trains; the second input quantizes the state of the return map and the IFM outputs various periodic pulse-trains. Using a computer aided analysis method, the quantized return map can be analyzed rigorously. Also, some typical phenomena are confirmed in the laboratory. key words: Integrate-and-Fire Model, return map, chaos, quantization, computer aided analysis
منابع مشابه
Bistability in a Leaky Integrate-and-Fire Neuron with a Passive Dendrite
We examine the influence of dendritic load on the firing dynamics of a spatially extended leaky integrate-and-fire (LIF) neuron that explicitly includes spiking dynamics. We obtain an exact analytical solution for this model and use it to derive a return map that completely captures the dynamics of the system. Using the map, we find that dendritic properties can significantly change the firing ...
متن کاملDynamical phase transitions in periodically driven model neurons.
Transitions between dynamical states in integrate-and-fire neuron models with periodic stimuli result from tangent or discontinuous bifurcations of a return map. We study their characteristic scaling laws and show that discontinuous bifurcations exhibit a kind of phase transition intermediate between continuous and first order. In the model-independent spirit of our analysis we show that a six-...
متن کاملPredicting and preparing a risk map of rangeland fires using random forest algorithms and support vector machine (Case study: Arak rangelands)
Abstract Background and objectives: Rangeland fires have devastating effects on the landscape, performance and services of rangeland ecosystems. Despite the efforts of experts, decision makers, stakeholders and government agencies in recent decades to reduce the effects of fire, its number and related economic and human losses are increasing worldwide. One of the most important measures to r...
متن کاملPeak-splitting in the Response of the Leaky Integrate-and-fire Neuron Model to Low-frequency Periodic Inputs
The cause of peak-splitting in the output phase distribution of the leaky integrate-and-fire single neuron model in response to low-frequency periodic nerve fibre inputs is analyzed. It is found that peaksplitting largely arises from an increase of the spiking-rate of individual nerve fibre inputs, or from an increase in amplitude of individual input excitatory postsynaptic potentials, or both....
متن کاملSwitched Dynamical Systems with Double Periodic Inputs: An Analysis Tool and Its Application to the Buck-Boost Converter
This paper considers a class of switched dynamical systems to which two periodic inputs are applicable. We derive a one-dimensional (1-D) return map and its derivative analytically for arbitrary shapes of the inputs. Based on the derivative, we introduce a slope chart that displays the relationship between the slope of the return map and that of the inputs. Applying the slope chart to a simplif...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999