Internal Decay Rate Research Articles

Chaotic single neuron model with periodic coefficients with period two

Our goal is to investigate the piecewise linear difference equation xn+1 = βnxn – g(xn). This piecewise linear difference equation is a prototype of one neuron model with the internal decay rate β and the signal function g. The authors investigated this model with periodic internal decay rate βn as a period-two sequence. Our aim is to show that for certain values of coefficients βn, there exists an attracting interval for which the model is chaotic. On the other hand, if the initial value is chosen outside the mentioned attracting interval, then the solution of the difference equation either increases to positive infinity or decreases to negative infinity.

High-cooperativity cavity magnon-polariton using a high-Qdielectric resonator

The hybrid system consisting of microwave photons and ferromagnetic magnons has been studied in the context of quantum sensing and quantum manipulation of magnons. We demonstrate a strong coupling between magnons and photons in a dielectric resonator with a large dielectric constant and high quality factor. The coupling rate between magnons and photons amounts to g/2π=126 MHz, and the corresponding cooperativity reaches C=1.09×106 at cryogenic temperature. The high cooperativity is mainly due to the small internal decay rate of the resonator, which is advantageous for various quantum magnonics experiments.

Eventually periodic solutions of single neuron model

In this paper, we consider a nonautonomous piecewise linear difference equation that describes a discrete version of a single neuron model with a periodic (period two and period three) internal decay rate. We investigated the periodic behavior of solutions relative to the periodic internal decay rate in our previous papers. Our goal is to prove that this model contains a large quantity of initial conditions that generate eventually periodic solutions. We will show that only periodic solutions and eventually periodic solutions exist in several cases.

Dissipative-coupling-assisted laser cooling: Limitations and perspectives

The recently identified possibility of ground-state cooling of a mechanical oscillator in the unresolved sideband regime by combination of the dissipative and dispersive optomechanical coupling under the red sideband excitation [Phys. Rev. A 88, 023850 (2013)], is currently viewed as a remarkable finding. We present a comprehensive analysis of this protocol, which reveals its very high sensitivity to small imperfections such as an additional dissipation, the inaccuracy of the optimized experimental settings, and the inaccuracy of the theoretical framework adopted. The impact of these imperfections on the cooling limit is quantitatively assessed. A very strong effect on the cooling limit is found from the internal cavity decay rate which even being small compared with the detection rate may drastically push that limit up, questioning the possibility of the ground state cooling. Specifically, the internal loss can only be neglected if the ratio of the internal decay rate to the detection rate is much smaller than the ratio of the cooling limit predicted by the protocol to the common dispersive-coupling assisted sideband cooling limit. More over, we establish that the condition of applicability of theory of that protocol is the requirement that the latter ratio is much smaller than one. A detailed comparison of the cooling protocol in question with the dispersive-coupling-assisted protocols which use the red sideband excitation or feedback is presented.

Neuron model with a period three internal decay rate

Neuron model with a period three internal decay rate

Periodic orbits of a neuron model with periodic internal decay rate

In this paper we will study a non-autonomous piecewise linear difference equation which describes a discrete version of a single neuron model with a periodic internal decay rate. We will investigate the periodic behavior of solutions relative to the periodic internal decay rate. Furthermore, we will show that only periodic orbits of even periods can exist and show their stability character.

PERIODIC ORBITS OF SINGLE NEURON MODELS WITH INTERNAL DECAY RATE 0 < Β ≤ 1

In this paper we consider a discrete dynamical system x n+1=βx n – g(x n ), n=0,1,..., arising as a discrete-time network of a single neuron, where 0 < β ≤ 1 is an internal decay rate, g is a signal function. A great deal of work has been done when the signal function is a sigmoid function. However, a signal function of McCulloch-Pitts nonlinearity described with a piecewise constant function is also useful in the modelling of neural networks. We investigate a more complicated step signal function (function that is similar to the sigmoid function) and we will prove some results about the periodicity of solutions of the considered difference equation. These results show the complexity of neurons behaviour.

Periodic solutions of difference equations

Consider the difference equation (∗) x n+1=βx n−g(x n),n=0,1,…, arising as a discrete-time network of single neuron, where β is the internal decay rate, g is a signal function with McCulloch–Pitts nonlinearity. For any positive integers k and m, necessary and sufficient conditions are obtained for ( ∗) has a periodic solution of period 2 k+1 or 2 m . In addition, sufficient conditions are also given for ( ∗) has a (2 k+1)2 m -periodic solution.

Periodic orbits on discrete dynamical systems

In this paper, we discuss the discrete dynamical system x n+1 = βx n − g( x n ), n = 0, 1, …, arising as a discrete-time network of single neuron, where β is the internal decay rate, g, is a signal function. First, we consider the case where g is of McCulloch-Pitts nonlinearity. Periodic orbits are discussed according to different range of β. Moreover, we can construct periodic orbits. Then, we consider the case where g is a sigmoid function. Sufficient conditions are obtained for (∗) has periodic orbits of arbitrary periods and an example is also given to illustrate the theorem.

Attractive Periodic Orbits in Nonlinear Discrete-time Neural Networks with Delayed Feedback

We consider the discrete-time system x ( n )= g x ( n m 1)+ f ( y ( n m k )), y ( n )= g y ( n m 1)+ f ( x ( n m k )), n ] N describing the dynamic interaction of two identical neurons, where g ] (0,1) is the internal decay rate, f is the signal transmission function and k is the signal transmission delay. We construct explicitly an attractive 2 k -periodic orbit in the case where f is a step function (McCulloch-Pitts Model). For the general nonlinear signal transmission functions, we use a perturbation argument and sharp estimates and apply the contractive map principle to obtain the existence and attractivity of a 2 k -periodic orbit. This is contrast to the continuous case (a delay differential system) where no stable periodic orbit can occur due to the monotonicity of the associated semiflow.