Abstract: We have designed a Holter that measures the heart´s activity for over 24 hours, implemented a prediction methodology, and generate alarms as well as indicators to patients and treating physicians. Various diagnostic advances have been developed in clinical cardiology thanks to Holter implementation; however, their interpretation has largely been conditioned to clinical analysis and measurements adjusted to diverse population characteristics, thus turning it into a subjective examination. This, however, requires vast population studies to be validated that, in turn, have not achieved the ultimate goal: mortality prediction. Given this context, our Insight Research Group developed a mathematical methodology that assesses cardiac dynamics through entropy and probability, creating a numerical and geometrical attractor which allows quantifying the normalcy of chronic and acute disease as well as the evolution between such states, and our Tigum Research Group developed a holter device with 12 channels and advanced computer software. This has been shown in different contexts with 100% sensitivity and specificity results.
Abstract: The mutual understanding in conversation is very important for human relations. This study investigates the mental function of the formation of mutual understanding between two people in conversation using the embodied approach. Forty people participated in this study. They are divided into pairs randomly. Four conversation situations between two (make/listen to fun or pleasant talk, make/listen to regrettable talk) are set for four minutes each, and the finger plethysmogram (200 Hz) of each participant is measured. As a result, the attractors of the participants who reported “I did not understand my partner” show the collapsed shape, which means the fluctuation of their rhythm is too small to match their partner’s rhythm, and their cross correlation is low. The autonomic balance of both persons tends to resonate during conversation, and both LLEs tend to resonate, too. In human history, in order for human beings as weak mammals to live, they may have been with others; that is, they have brought about resonating characteristics, which is called self-organization. However, the resonant feature sometimes collapses, depending on the lifestyle that the person was formed by himself after birth. It is difficult for people who do not have a lifestyle of mutual gaze to resonate their biological signal waves with others’. These people have features such as anxiety, fatigue, and confusion tendency. Mutual understanding is thought to be formed as a result of cooperation between the features of self-organization of the persons who are talking and the lifestyle indicated by mutual gaze. Such an entanglement phenomenon is called a nonlinear relation. By this research, it is found that the formation of mutual understanding is expressed by the rhythm of a biological signal showing a nonlinear relationship.
Abstract: In this paper, an encryption algorithm is proposed for real-time image encryption. The scheme employs a dual chaotic generator based on a three dimensional (3D) discrete Lorenz attractor. Encryption is achieved using non-autonomous modulation where the data is injected into the dynamics of the master chaotic generator. The second generator is used to permute the dynamics of the master generator using the same approach. Since the data stream can be regarded as a random source, the resulting permutations of the generator dynamics greatly increase the security of the transmitted signal. In addition, a technique is proposed to mitigate the error propagation due to the finite precision arithmetic of digital hardware. In particular, truncation and rounding errors are eliminated by employing an integer representation of the data which can easily be implemented. The simple hardware architecture of the algorithm makes it suitable for secure real-time applications.
Abstract: In this report we have discussed the theoretical aspects
of the flow transformation, occurring through a series of bifurcations.
The parameters and their continuous diversion, the intermittent bursts
in the transition zone, variation of velocity and pressure with time,
effect of roughness in turbulent zone, and changes in friction factor
and head loss coefficient as a function of Reynolds number for a
transverse flow across a cylinder have been discussed. An analysis of
the variation in the wake length with Reynolds number was done in
FORTRAN.
Abstract: An Ivlev-type predator-prey system and stage-structured for predator concerning impulsive control strategy is considered. The conditions for the locally asymptotically stable prey-eradication periodic solution is obtained, by using Floquet theorem and small amplitude perturbation skills——when the impulsive period is less than the critical value. Otherwise, the system is permanence. Numerical examples show that the system considered has more complicated dynamics, including high-order quasi-periodic and periodic oscillating, period-doubling and period-halving bifurcation, chaos and attractor crisis, etc. Finally, the biological implications of the results and the impulsive control strategy are discussed.
Abstract: This document shows a software that shows different chaotic generator, as continuous as discrete time. The software gives the option for obtain the different signals, using different parameters and initial condition value. The program shows then critical parameter for each model. All theses models are capable of encrypter information, this software show it too.
Abstract: Deep Brain Stimulation or DBS is a surgical treatment for Parkinson-s Disease with three stimulation parameters: frequency, pulse width, and voltage. The parameters should be selected appropriately to achieve effective treatment. This selection now, performs clinically. The aim of this research is to study chaotic behavior of recorded tremor of patients under DBS in order to present a computational method to recognize stimulation optimum voltage. We obtained some chaotic features of tremor signal, and discovered embedding space of it has an attractor, and its largest Lyapunov exponent is positive, which show tremor signal has chaotic behavior, also we found out, in optimal voltage, entropy and embedding space variance of tremor signal have minimum values in comparison with other voltages. These differences can help neurologists recognize optimal voltage numerically, which leads to reduce patients' role and discomfort in optimizing stimulation parameters and to do treatment with high accuracy.
Abstract: The model of neural networks on the small-world
topology, with metric (local and random connectivity) is investigated.
The synaptic weights are random, driving the network towards a
chaotic state for the neural activity. An ordered macroscopic neuron
state is induced by a bias in the network connections. When the
connections are mainly local, the network emulates a block-like
structure. It is found that the topology and the bias compete to
influence the network to evolve into a global or a block activity
ordering, according to the initial conditions.
Abstract: DC-DC converters are widely used in regulated switched mode power supplies and in DC motor drive applications. There are several sources of unwanted nonlinearity in practical power converters. In addition, their operation is characterized by switching that gives birth to a variety of nonlinear dynamics. DC-DC buck and boost converters controlled by pulse-width modulation (PWM) have been simulated. The voltage waveforms and attractors obtained from the circuit simulation have been studied. With the onset of instability, the phenomenon of subharmonic oscillations, quasi-periodicity, bifurcations, and chaos have been observed. This paper is mainly motivated by potential contributions of chaos theory in the design, analysis and control of power converters, in particular and power electronics circuits, in general.
Abstract: In this paper, we investigate dynamics of 2n almost periodic attractors for Cohen-Grossberg neural networks (CGNNs) with variable and distribute time delays. By imposing some new assumptions on activation functions and system parameters, we split invariant basin of CGNNs into 2n compact convex subsets. Then the existence of 2n almost periodic solutions lying in compact convex subsets is attained due to employment of the theory of exponential dichotomy and Schauder-s fixed point theorem. Meanwhile, we derive some new criteria for the networks to converge toward these 2n almost periodic solutions and exponential attracting domains are also given correspondingly.
Abstract: Measures of complexity and entropy have not converged to a single quantitative description of levels of organization of complex systems. The need for such a measure is increasingly necessary in all disciplines studying complex systems. To address this problem, starting from the most fundamental principle in Physics, here a new measure for quantity of organization and rate of self-organization in complex systems based on the principle of least (stationary) action is applied to a model system - the central processing unit (CPU) of computers. The quantity of organization for several generations of CPUs shows a double exponential rate of change of organization with time. The exact functional dependence has a fine, S-shaped structure, revealing some of the mechanisms of self-organization. The principle of least action helps to explain the mechanism of increase of organization through quantity accumulation and constraint and curvature minimization with an attractor, the least average sum of actions of all elements and for all motions. This approach can help describe, quantify, measure, manage, design and predict future behavior of complex systems to achieve the highest rates of self organization to improve their quality. It can be applied to other complex systems from Physics, Chemistry, Biology, Ecology, Economics, Cities, network theory and others where complex systems are present.
Abstract: The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.
Abstract: In the context of channel coding, the Generalized Belief Propagation (GBP) is an iterative algorithm used to recover the transmission bits sent through a noisy channel. To ensure a reliable transmission, we apply a map on the bits, that is called a code. This code induces artificial correlations between the bits to send, and it can be modeled by a graph whose nodes are the bits and the edges are the correlations. This graph, called Tanner graph, is used for most of the decoding algorithms like Belief Propagation or Gallager-B. The GBP is based on a non unic transformation of the Tanner graph into a so called region-graph. A clear advantage of the GBP over the other algorithms is the freedom in the construction of this graph. In this article, we explain a particular construction for specific graph topologies that involves relevant performance of the GBP. Moreover, we investigate the behavior of the GBP considered as a dynamic system in order to understand the way it evolves in terms of the time and in terms of the noise power of the channel. To this end we make use of classical measures and we introduce a new measure called the hyperspheres method that enables to know the size of the attractors.
Abstract: The nonlinear chaotic non-autonomous fourth order
system is algebraically simple but can generate complex chaotic
attractors. In this paper, non-autonomous fourth order chaotic
oscillator circuits were designed and simulated. Also chaotic nonautonomous
Attractor is addressed suitable for chaotic masking
communication circuits using Matlab® and MultiSIM® programs.
We have demonstrated in simulations that chaos can be synchronized
and applied to signal masking communications. We suggest that this
phenomenon of chaos synchronism may serve as the basis for little
known chaotic non-autonomous Attractor to achieve signal masking
communication applications. Simulation results are used to visualize
and illustrate the effectiveness of non-autonomous chaotic system in
signal masking. All simulations results performed on nonautonomous
chaotic system are verify the applicable of secure
communication.
Abstract: Recognizing behavioral patterns of financial markets
is essential for traders. Japanese candlestick chart is a common tool to
visualize and analyze such patterns in an economic time series. Since
the world was introduced to Japanese candlestick charting, traders
saw how combining this tool with intelligent technical approaches
creates a powerful formula for the savvy investors.
This paper propose a generalization to box counting method of
Grassberger-Procaccia, which is based on computing the correlation
dimension of Japanese candlesticks instead commonly used 'close'
points. The results of this method applied on several foreign
exchange rates vs. IRR (Iranian Rial). Satisfactorily show lower
chaotic dimension of Japanese candlesticks series than regular
Grassberger-Procaccia method applied merely on close points of
these same candles. This means there is some valuable information
inside candlesticks.
Abstract: Since 1984 many schemes have been proposed for
digital signature protocol, among them those that based on discrete
log and factorizations. However a new identification scheme based
on iterated function (IFS) systems are proposed and proved to be
more efficient. In this study the proposed identification scheme is
transformed into a digital signature scheme by using a one way hash
function. It is a generalization of the GQ signature schemes. The
attractor of the IFS is used to obtain public key from a private one,
and in the encryption and decryption of a hash function. Our aim is
to provide techniques and tools which may be useful towards
developing cryptographic protocols. Comparisons between the
proposed scheme and fractal digital signature scheme based on RSA
setting, as well as, with the conventional Guillou-Quisquater
signature, and RSA signature schemes is performed to prove that, the
proposed scheme is efficient and with high performance.
Abstract: The aim of this paper is to propose a mathematical
model to determine invariant sets, set covering, orbits and, in
particular, attractors in the set of tourism variables. Analysis was
carried out based on a pre-designed algorithm and applying our
interpretation of chaos theory developed in the context of General
Systems Theory. This article sets out the causal relationships
associated with tourist flows in order to enable the formulation of
appropriate strategies. Our results can be applied to numerous cases.
For example, in the analysis of tourist flows, these findings can be
used to determine whether the behaviour of certain groups affects that
of other groups and to analyse tourist behaviour in terms of the most
relevant variables. Unlike statistical analyses that merely provide
information on current data, our method uses orbit analysis to
forecast, if attractors are found, the behaviour of tourist variables in
the immediate future.
Abstract: In this paper, stability and Hopf bifurcation analysis of
a novel hyperchaotic system are investigated. Four feedback control
strategies, the linear feedback control method, enhancing feedback
control method, speed feedback control method and delayed feedback
control method, are used to control the hyperchaotic attractor to
unstable equilibrium. Moreover numerical simulations are given to
verify the theoretical results.
Abstract: Daily production of information and importance of the sequence of produced data in forecasting future performance of market causes analysis of data behavior to become a problem of analyzing time series. But time series that are very complicated, usually are random and as a result their changes considered being unpredictable. While these series might be products of a deterministic dynamical and nonlinear process (chaotic) and as a result be predictable. Point of Chaotic theory view, complicated systems have only chaotically face and as a result they seem to be unregulated and random, but it is possible that they abide by a specified math formula. In this article, with regard to test of strange attractor and biggest Lyapunov exponent probability of chaos on several foreign exchange rates vs. IRR (Iranian Rial) has been investigated. Results show that data in this market have complex chaotic behavior with big degree of freedom.
Abstract: A systems approach model for prostate cancer in prostate duct, as a sub-system of the organism is developed. It is accomplished in two steps. First this research work starts with a nonlinear system of coupled Fokker-Plank equations which models continuous process of the system like motion of cells. Then extended to PDEs that include discontinuous processes like cell mutations, proliferation and deaths. The discontinuous processes is modeled by using intensity poisson processes. The model incorporates the features of the prostate duct. The system of PDEs spatial coordinate is along the proximal distal axis. Its parameters depend on features of the prostate duct. The movement of cells is biased towards distal region and mutations of prostate cancer cells is localized in the proximal region. Numerical solutions of the full system of equations are provided, and are exhibit traveling wave fronts phenomena. This motivates the use of the standard transformation to derive a canonically related system of ODEs for traveling wave solutions. The results obtained show persistence of prostate cancer by showing that the non-negative cone for the traveling wave system is time invariant. The traveling waves have a unique global attractor is proved also. Biologically, the global attractor verifies that evolution of prostate cancer stem cells exhibit the avascular tumor growth. These numerical solutions show that altering prostate stem cell movement or mutation of prostate cancer cells lead to avascular tumor. Conclusion with comments on clinical implications of the model is discussed.