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

Construction of chaotic dynamical system

The first‐order difference equation xn+ 1 = f(xn ), n = 0,1,…, where f: R → R, is referred as an one‐dimensional discrete dynamical system. If function f is a chaotic mapping, then we talk about chaotic dynamical system. Models with chaotic mappings are not predictable in long‐term. In this paper we consider family of chaotic mappings in symbol space S 2. We use the idea of topological semi‐conjugacy and so we can construct a family of mappings in the unit segment such that it is chaotic. First published online: 09 Jun 201

Neuron model with a period three internal decay rate

In this paper we will study a non-autonomous piecewise linear difference equation that describes a discrete version of a single neuron model. We will investigate the periodic behavior of solutions relative to the sequence periodic with period three internal decay rate. In fact, we will show that only periodic cycles with period $3k$, $k=1,2,3,\dots$ can exist and also show their stability character

Periodic and Chaotic Orbits of a Neuron Model

In this paper we study a class of difference equations which describes a discrete version of a single neuron model. We consider a generalization of the original McCulloch-Pitts model that has two thresholds. Periodic orbits are investigated accordingly to the different range of parameters. For some parameters sufficient conditions for periodic orbits of arbitrary periods have been obtained. We conclude that there exist values of parameters such that the function in the model has chaotic orbits. Models with chaotic orbits are not predictable in long-term

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

How to Check Continuity Based on Approximate Measurement Results

In many practical situations, a reasonable conjecture is that, e.g., the dependence of some quantity on the spatial location is continuous, with an appropriate bounds on the difference between the values at nearby points. If we knew the exact values of the corresponding quantity, checking this conjecture would be very straightforward. In reality, however, measurement results are only approximations to the actual values. In this paper, we show how to check continuity based on the approximate measurement results

Exercise to Promote Pupil Securitability

Health and safety is based on the choices that people make during lifetime. Each of us chooses to act safely or unsafely, healthy or unhealthy. Specific risk group is children and youngsters. Children and young people often have a desire to test their independence, build a personal identity and expand the social life, so young people often experiment also with different types of behavior. In the situations not favorable to health and safety children and young people behavior often do not comply with their knowledge of how to act. Human (human securitability is an internationally-known concept that characterizes human adaptability skills in a rapidly changing environment. Are distinguished 7 human securitability aspects: health, economic, personal (physical), ecological securitability, nutritional, community and political securitability. In the National development plan (NDP) 2020 strategy one of the priorities is human securitability provision. In our study, we analyzed the personal (physical) securitability of educational institutions. A person with a low sense of securitability feels threatened, does not want to use the opportunities of personal growth, trust others and cooperate with them at workplace and in collectives, does not want to participate in the state national development process, and therefore does not contribute to national growth. The pupils are able to learn successfully at school, develop their ability to form a personality only in an environment with a sustainable securitability. The pupil parents can successfully work and act only in the case they are absolutely certain about their children securitability at school, where they spend most of the working day: at schools, in after-school hobby groups, in sports trainings. Creating a safe environment at schools and being educated, growing and developing in this environment, the pupils form understanding of the necessity for a safe and healthy environment and its importance, and develop motivation to keep it for the needs of family, society and the public. In strengthening securitability equally important is knowledge and skills to act in different situations. Researching education policy documents, the authors draw the conclusion that it is necessary on a state level to strengthen the securitability of each Latvian resident and the issues related to state securitability in educational institutions and society as a whole. Sports teacher can contribute to the promotion of pupil securitability, using the subject content as the means. Human securitability can be promoted by knowledge acquisition and skills development in securitability-oriented sports lesson

Neuron model with a period three internal decay rate

In this paper we will study a non-autonomous piecewise linear difference equation that describes a discrete version of a single neuron model. We will investigate the periodic behavior of solutions relative to the sequence periodic with period three internal decay rate. In fact, we will show that only periodic cycles with period $3k$, $k=1,2,3,\dots$ can exist and also 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&nbsp;n+1=βx&nbsp;n&nbsp;–&nbsp;g(x&nbsp;n&nbsp;),&nbsp;n=0,1,..., arising as a discrete-time network of a single neuron, where 0 &lt;&nbsp;β&nbsp;≤ 1 is an internal decay rate,&nbsp;g&nbsp;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