Revista de Matemática: Teoría y Aplicaciones, 2017
Para analizar la estabilidad de un sistema de ecuaciones diferenciales lineales ẋ = Ax podemos e... more Para analizar la estabilidad de un sistema de ecuaciones diferenciales lineales ẋ = Ax podemos estudiar la localización de las raíces del polinomio característico pA(t) asociado a la matriz A. En este artículo presentamos diversos criterios —algebraicos y geométricos— que nos ayudan a determinar el lugar donde se encuentran las raíces sin necesidad de calcularlas en forma directa.
Progeny were generated in two spawning seasons (2002 and 2003) in a fully pedigreed population ba... more Progeny were generated in two spawning seasons (2002 and 2003) in a fully pedigreed population based on the sixth generation of GIFT (Genetically Improved Farmed Tilapia) established in Malaysia. Two lines were created (Selection and Control), and two production environments (cages and ponds) were used to grow out the fish. Live weight at harvest (LW) was the trait under selection, treating the production environments as a fixed effect in the model. In the analysis presented here LW in cages and in ponds was treated as two different traits (LWC and LWP, respectively). Response to selection was estimated for LWC and LWP by three methods by comparing: (i) The least squares means of LW for the Selection and Control lines in the progeny of the 2003 spawning season, (ii) The estimated breeding values for LW between the progeny of the 2002 spawning season and those of the Selected line in the 2003 spawning season, and (iii) The estimated breeding values of the Selection and Control lines in progeny of the 2003 spawning season. For LWC, expressed as a percentage of the overall least squares mean in the population, the estimates were 9.2, 9.6 and 12.7 for methods (i), (ii) and (iii), whereas for LWP they were 8.2, 7.9 and 10.4, respectively. It was concluded that selection response was being achieved in both environments and that there was not enough evidence to justify the conduct of separate genetic improvement programs for cage and pond environments.
Dynamical systems methods have been recently used in spread-spectrum digital communication system... more Dynamical systems methods have been recently used in spread-spectrum digital communication systems. Theexpansion of the spectrum using a pseudorandom sequence with a higher frequency than the information signal is thekey feature for its robustness against the signal traveling interference through the channel. In this work, we propose togenerate pseudorandom sequences by employing cellular automata and we check these sequences have thenecessary properties which are required in modern communication systems. The computed sequences obtained bythe cellular automata are tested in a quadrature phase shift keying (QPSK) spread-spectrum communication system.The efficiency of the system is analyzed by computing the bit error rate under different signal to noise ratio conditions.These results are compared with systems that employ Golden code and other typical pseudorandom sequences.
In this work, we present a simple algorithm to design n × n-bits substitution boxes (S-boxes) bas... more In this work, we present a simple algorithm to design n × n-bits substitution boxes (S-boxes) based on chaotic time series of the logistic map for different carrying capacities. The use of different carrying capacities in the chaotic map leads to low computational complexity, which is desirable to get high-speed communication systems. We generate a main sequence by means of two auxiliary sequences with uniform distribution via the logistic map for different carrying capacities. The elements of the main sequence are useful for generating the elements of an S-box. The auxiliary sequences are generated by considering lag time chaotic series; this helps to hide the chaotic map used. The U-shape distribution of logistic chaotic map is also avoided, in contrast with common chaos-based schemes without considering lag time chaotic series, and uncorrelated S-box elements are obtained. The proposed algorithm guarantees the generation of strong S-boxes that fulfill the following criteria: bije...
We pres ent ex per i men tal re sults of a cha otic com mu ni ca tion sys tem that em ploys di re... more We pres ent ex per i men tal re sults of a cha otic com mu ni ca tion sys tem that em ploys di rect mod u la tion, with the Chua's cha otic os cil la tor as a core of the trans mit ter block. The main re sult is that its pos si ble to re cover the in for ma tion sig nal if we mod u late over one state of os cil la tor and trans mit a dif fer ent state, avoid ing a cor re la tion be tween the in for ma tion sig nal and the cha otic carrier.
In the framework of robust stability analysis of linear systems, the development of techniques an... more In the framework of robust stability analysis of linear systems, the development of techniques and methods that help to obtain necessary and sufficient conditions to determine stability of convex combinations of polynomials is paramount. In this paper, knowing that Hurwitz polynomials set is not a convex set, a brief overview of some results and open problems concerning the stability of the convex combinations of Hurwitz polynomials is then provided.
En este trabajo se analizan series de tiempo con dinámica caótica provenientes de un sistema de c... more En este trabajo se analizan series de tiempo con dinámica caótica provenientes de un sistema de comunicación. El análisis se realiza con la transformada ondoleta ortogonal, la cual nos proporciona información sobre la distribución de energía en los diferentes niveles ondoleta de las series de tiempo. Además, se establece la regiónútil en función de la amplitud y frecuencia de la señal de información a ser transmitida. Descriptores: Series de tiempo caóticas; sistema de comunicación; ondoletas. In this paper we analyze time series with chaotic dynamics from a communication system. The analysis is performed with the orthogonal wavelet transform, which gives us information about of energy distribution in the different wavelet levels from the time series. Furthermore, It is established the useful region as a function of the amplitude and frequency values of the information signal to be transmitted.
International Journal of Bifurcation and Chaos, 2010
We report experimental results obtained with a circuit possessing dynamic logic architecture base... more We report experimental results obtained with a circuit possessing dynamic logic architecture based on one of the theoretical schemes proposed by H. Peng and collaborators in 2008. The schematic diagram of the electronic circuit and its implementation to get different basic logic gates are displayed and discussed. In particular, we show explicitly how to get the electronic NOR, NAND and XOR gates. The proposed electronic circuit is easy to build because it employs only resistors, operational amplifiers and comparators.
In nature, an interesting topic is about how a cell can be reconfigured in order to achieve a dif... more In nature, an interesting topic is about how a cell can be reconfigured in order to achieve a different task. Another interesting topic is about the learning process that seems to be a trial and error process. In this work, we present mechanisms about how to produce a reconfigurable logical cell based on the tent map. The reconfiguration is realized by modifying its internal parameters generating several logical functions in the same structure. The logical cell is built with three blocks: the initial condition generating function, the tent map, and the output function. Furthermore, we propose a reconfigurable structure based on a chaotic system and an evolutionary algorithm is used in order to tune the parameters of the cell via trial and error process.
We present a very simple electronic implementation of the tent map, one of the best-known discret... more We present a very simple electronic implementation of the tent map, one of the best-known discrete dynamical systems. This is achieved by using integrated circuits and passive elements only. The experimental behavior of the tent map electronic circuit is compared with its numerical simulation counterpart. We find that the electronic circuit presents fixed points, periodicity, period doubling, chaos and intermittency that match with high accuracy the corresponding theoretical values.
We present a study on a class of interconnected nonlinear systems and give some criteria for them... more We present a study on a class of interconnected nonlinear systems and give some criteria for them to behave like a filter. Some chaotic systems present this kind of interconnected nonlinear structure, which enables the synchronization of a master-slave system. Interconnected nonlinear filters have been defined in terms of interconnected nonlinear systems. Furthermore, their behaviors have been studied numerically and theoretically on different input signals.
Analog Integrated Circuits and Signal Processing, 2010
This paper describes a signal generator based on Chua's circuit in order to obtain some know wave... more This paper describes a signal generator based on Chua's circuit in order to obtain some know wave forms: chaotic, sine, square and triangle signals, with the possibility to generate other types of waves in others forms. The results are tested experimentally. The hardware implementation of the signal generator is very simple.
The equation of the plane (EOP) in analytic geometry is used to build a logic dynamic architectur... more The equation of the plane (EOP) in analytic geometry is used to build a logic dynamic architecture, i.e., a combination of set-reset flip flop (SR-FF) and basic logic gates. This is achieved by using two of the variables in the EOP as the input signals of the SR-FF and the remaining variable as the output signal. This theoretical proposal for mixing the SR-FF and the basic logic gates is confirmed experimentally by means of a simple electronic implementation.
In this paper, we present a study of the diffusion properties of a deterministic model for settli... more In this paper, we present a study of the diffusion properties of a deterministic model for settling particles in two displacement dimensions. The particularities of the novel deterministic model include the generation of Brownian motion and a two-dimensional displacement model without stochastic processes, which are governed by a set of six differential equations. This model is a piecewise system consisting of subsystems governed by jerk equations. With this model, we can consider different conditions of diffusion in both the dimensions and size of the space where the particles are dispersed. The settling time versus the dispersion medium and its size, as well as the average settling time and its probability distributions, are analyzed. Furthermore, the probability distributions for the settling location are presented for the changes in the diffusion parameters and space size. Finally, the basins of attraction for the settling positions are shown as a function of each dimensional di...
The employment of chaotic maps in a variety of applications such as cryptosecurity, image encrypt... more The employment of chaotic maps in a variety of applications such as cryptosecurity, image encryption schemes, communication schemes, and secure communication has been made possible thanks to their properties of high levels of complexity, ergodicity, and high sensitivity to the initial conditions, mainly. Of considerable interest is the implementation of these dynamical systems in electronic devices such as field programmable gate arrays (FPGAs) with the intention of experimentally reproducing their dynamics, leading to exploiting their chaotic properties in real phenomena. In this work, the implementation of a one-dimensional chaotic map that has no fixed points is performed on an FPGA device with the objective of being able to reproduce its chaotic behavior as well as possible. The chaotic behavior of the introduced system is determined by estimating the Lyapunov exponents and its chaotic behavior is also analyzed using bifurcation diagrams. Simulations of the system are realized v...
Revista de Matemática: Teoría y Aplicaciones, 2017
Para analizar la estabilidad de un sistema de ecuaciones diferenciales lineales ẋ = Ax podemos e... more Para analizar la estabilidad de un sistema de ecuaciones diferenciales lineales ẋ = Ax podemos estudiar la localización de las raíces del polinomio característico pA(t) asociado a la matriz A. En este artículo presentamos diversos criterios —algebraicos y geométricos— que nos ayudan a determinar el lugar donde se encuentran las raíces sin necesidad de calcularlas en forma directa.
Progeny were generated in two spawning seasons (2002 and 2003) in a fully pedigreed population ba... more Progeny were generated in two spawning seasons (2002 and 2003) in a fully pedigreed population based on the sixth generation of GIFT (Genetically Improved Farmed Tilapia) established in Malaysia. Two lines were created (Selection and Control), and two production environments (cages and ponds) were used to grow out the fish. Live weight at harvest (LW) was the trait under selection, treating the production environments as a fixed effect in the model. In the analysis presented here LW in cages and in ponds was treated as two different traits (LWC and LWP, respectively). Response to selection was estimated for LWC and LWP by three methods by comparing: (i) The least squares means of LW for the Selection and Control lines in the progeny of the 2003 spawning season, (ii) The estimated breeding values for LW between the progeny of the 2002 spawning season and those of the Selected line in the 2003 spawning season, and (iii) The estimated breeding values of the Selection and Control lines in progeny of the 2003 spawning season. For LWC, expressed as a percentage of the overall least squares mean in the population, the estimates were 9.2, 9.6 and 12.7 for methods (i), (ii) and (iii), whereas for LWP they were 8.2, 7.9 and 10.4, respectively. It was concluded that selection response was being achieved in both environments and that there was not enough evidence to justify the conduct of separate genetic improvement programs for cage and pond environments.
Dynamical systems methods have been recently used in spread-spectrum digital communication system... more Dynamical systems methods have been recently used in spread-spectrum digital communication systems. Theexpansion of the spectrum using a pseudorandom sequence with a higher frequency than the information signal is thekey feature for its robustness against the signal traveling interference through the channel. In this work, we propose togenerate pseudorandom sequences by employing cellular automata and we check these sequences have thenecessary properties which are required in modern communication systems. The computed sequences obtained bythe cellular automata are tested in a quadrature phase shift keying (QPSK) spread-spectrum communication system.The efficiency of the system is analyzed by computing the bit error rate under different signal to noise ratio conditions.These results are compared with systems that employ Golden code and other typical pseudorandom sequences.
In this work, we present a simple algorithm to design n × n-bits substitution boxes (S-boxes) bas... more In this work, we present a simple algorithm to design n × n-bits substitution boxes (S-boxes) based on chaotic time series of the logistic map for different carrying capacities. The use of different carrying capacities in the chaotic map leads to low computational complexity, which is desirable to get high-speed communication systems. We generate a main sequence by means of two auxiliary sequences with uniform distribution via the logistic map for different carrying capacities. The elements of the main sequence are useful for generating the elements of an S-box. The auxiliary sequences are generated by considering lag time chaotic series; this helps to hide the chaotic map used. The U-shape distribution of logistic chaotic map is also avoided, in contrast with common chaos-based schemes without considering lag time chaotic series, and uncorrelated S-box elements are obtained. The proposed algorithm guarantees the generation of strong S-boxes that fulfill the following criteria: bije...
We pres ent ex per i men tal re sults of a cha otic com mu ni ca tion sys tem that em ploys di re... more We pres ent ex per i men tal re sults of a cha otic com mu ni ca tion sys tem that em ploys di rect mod u la tion, with the Chua's cha otic os cil la tor as a core of the trans mit ter block. The main re sult is that its pos si ble to re cover the in for ma tion sig nal if we mod u late over one state of os cil la tor and trans mit a dif fer ent state, avoid ing a cor re la tion be tween the in for ma tion sig nal and the cha otic carrier.
In the framework of robust stability analysis of linear systems, the development of techniques an... more In the framework of robust stability analysis of linear systems, the development of techniques and methods that help to obtain necessary and sufficient conditions to determine stability of convex combinations of polynomials is paramount. In this paper, knowing that Hurwitz polynomials set is not a convex set, a brief overview of some results and open problems concerning the stability of the convex combinations of Hurwitz polynomials is then provided.
En este trabajo se analizan series de tiempo con dinámica caótica provenientes de un sistema de c... more En este trabajo se analizan series de tiempo con dinámica caótica provenientes de un sistema de comunicación. El análisis se realiza con la transformada ondoleta ortogonal, la cual nos proporciona información sobre la distribución de energía en los diferentes niveles ondoleta de las series de tiempo. Además, se establece la regiónútil en función de la amplitud y frecuencia de la señal de información a ser transmitida. Descriptores: Series de tiempo caóticas; sistema de comunicación; ondoletas. In this paper we analyze time series with chaotic dynamics from a communication system. The analysis is performed with the orthogonal wavelet transform, which gives us information about of energy distribution in the different wavelet levels from the time series. Furthermore, It is established the useful region as a function of the amplitude and frequency values of the information signal to be transmitted.
International Journal of Bifurcation and Chaos, 2010
We report experimental results obtained with a circuit possessing dynamic logic architecture base... more We report experimental results obtained with a circuit possessing dynamic logic architecture based on one of the theoretical schemes proposed by H. Peng and collaborators in 2008. The schematic diagram of the electronic circuit and its implementation to get different basic logic gates are displayed and discussed. In particular, we show explicitly how to get the electronic NOR, NAND and XOR gates. The proposed electronic circuit is easy to build because it employs only resistors, operational amplifiers and comparators.
In nature, an interesting topic is about how a cell can be reconfigured in order to achieve a dif... more In nature, an interesting topic is about how a cell can be reconfigured in order to achieve a different task. Another interesting topic is about the learning process that seems to be a trial and error process. In this work, we present mechanisms about how to produce a reconfigurable logical cell based on the tent map. The reconfiguration is realized by modifying its internal parameters generating several logical functions in the same structure. The logical cell is built with three blocks: the initial condition generating function, the tent map, and the output function. Furthermore, we propose a reconfigurable structure based on a chaotic system and an evolutionary algorithm is used in order to tune the parameters of the cell via trial and error process.
We present a very simple electronic implementation of the tent map, one of the best-known discret... more We present a very simple electronic implementation of the tent map, one of the best-known discrete dynamical systems. This is achieved by using integrated circuits and passive elements only. The experimental behavior of the tent map electronic circuit is compared with its numerical simulation counterpart. We find that the electronic circuit presents fixed points, periodicity, period doubling, chaos and intermittency that match with high accuracy the corresponding theoretical values.
We present a study on a class of interconnected nonlinear systems and give some criteria for them... more We present a study on a class of interconnected nonlinear systems and give some criteria for them to behave like a filter. Some chaotic systems present this kind of interconnected nonlinear structure, which enables the synchronization of a master-slave system. Interconnected nonlinear filters have been defined in terms of interconnected nonlinear systems. Furthermore, their behaviors have been studied numerically and theoretically on different input signals.
Analog Integrated Circuits and Signal Processing, 2010
This paper describes a signal generator based on Chua's circuit in order to obtain some know wave... more This paper describes a signal generator based on Chua's circuit in order to obtain some know wave forms: chaotic, sine, square and triangle signals, with the possibility to generate other types of waves in others forms. The results are tested experimentally. The hardware implementation of the signal generator is very simple.
The equation of the plane (EOP) in analytic geometry is used to build a logic dynamic architectur... more The equation of the plane (EOP) in analytic geometry is used to build a logic dynamic architecture, i.e., a combination of set-reset flip flop (SR-FF) and basic logic gates. This is achieved by using two of the variables in the EOP as the input signals of the SR-FF and the remaining variable as the output signal. This theoretical proposal for mixing the SR-FF and the basic logic gates is confirmed experimentally by means of a simple electronic implementation.
In this paper, we present a study of the diffusion properties of a deterministic model for settli... more In this paper, we present a study of the diffusion properties of a deterministic model for settling particles in two displacement dimensions. The particularities of the novel deterministic model include the generation of Brownian motion and a two-dimensional displacement model without stochastic processes, which are governed by a set of six differential equations. This model is a piecewise system consisting of subsystems governed by jerk equations. With this model, we can consider different conditions of diffusion in both the dimensions and size of the space where the particles are dispersed. The settling time versus the dispersion medium and its size, as well as the average settling time and its probability distributions, are analyzed. Furthermore, the probability distributions for the settling location are presented for the changes in the diffusion parameters and space size. Finally, the basins of attraction for the settling positions are shown as a function of each dimensional di...
The employment of chaotic maps in a variety of applications such as cryptosecurity, image encrypt... more The employment of chaotic maps in a variety of applications such as cryptosecurity, image encryption schemes, communication schemes, and secure communication has been made possible thanks to their properties of high levels of complexity, ergodicity, and high sensitivity to the initial conditions, mainly. Of considerable interest is the implementation of these dynamical systems in electronic devices such as field programmable gate arrays (FPGAs) with the intention of experimentally reproducing their dynamics, leading to exploiting their chaotic properties in real phenomena. In this work, the implementation of a one-dimensional chaotic map that has no fixed points is performed on an FPGA device with the objective of being able to reproduce its chaotic behavior as well as possible. The chaotic behavior of the introduced system is determined by estimating the Lyapunov exponents and its chaotic behavior is also analyzed using bifurcation diagrams. Simulations of the system are realized v...
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