Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a “buffer” cell, with Z3×Z5 symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a few. The different patterns seem to arise through a sequence of Hopf bifurcations, period-doubling, and halving-period bifurcations. The network architecture seems to explain certain observed features, such as equilibria and the rotating waves, whereas the properties of the chaotic oscillator may explain others, such as the quasiperiodic and chaotic states. We use XPPAUT and MATLAB to compute numerically the relevant states.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

Complex order biped rhythms

Animal locomotion is a complex process, involving the central pattern generators (neural networks, located in the spinal cord, that produce rhythmic patterns), the brainstem command systems, the steering and posture control systems and the top layer structures that decide which motor primitive is activated at a given time. Pinto and Golubitsky studied an integer CPG model for legs rhythms in bipeds. It is a four-coupled identical oscillators' network with dihedral symmetry. This paper considers a new complex order central pattern generator (CPG) model for locomotion in bipeds. A complex derivative Dα±jβ, with α, β ∈ ℜ+, j = √-1, is a generalization of the concept of an integer derivative, where α = 1, β = 0. Parameter regions where periodic solutions, identified with legs' rhythms in bipeds, occur, are analyzed. Also observed is the variation of the amplitude and period of periodic solutions with the complex order derivative.

Fractional central pattern generators for bipedal locomotion

Locomotion has been a major research issue in the last few years. Many models for the locomotion rhythms of quadrupeds, hexapods, bipeds and other animals have been proposed. This study has also been extended to the control of rhythmic movements of adaptive legged robots. In this paper, we consider a fractional version of a central pattern generator (CPG) model for locomotion in bipeds. A fractional derivative D α f(x), with α non-integer, is a generalization of the concept of an integer derivative, where α=1. The integer CPG model has been proposed by Golubitsky, Stewart, Buono and Collins, and studied later by Pinto and Golubitsky. It is a network of four coupled identical oscillators which has dihedral symmetry. We study parameter regions where periodic solutions, identified with legs’ rhythms in bipeds, occur, for 0<α≤1. We find that the amplitude and the period of the periodic solutions, identified with biped rhythms, increase as α varies from near 0 to values close to unity.

Electrochemical immunosensor for the analysis of the breast cancer biomarker HER2 ECD

Human epidermal growth factor receptor 2 (HER2) is a breast cancer biomarker that plays a major role in promoting breast cancer cell proliferation and malignant growth. The extracellular domain (ECD) of HER2 can be shed into the blood stream and its concentration is measurable in the serum fraction of blood. In this work an electrochemical immunosensor for the analysis of HER2 ECD in human serum samples was developed. To achieve this goal a screen-printed carbon electrode, modified with gold nanoparticles, was used as transducer surface. A sandwich immunoassay, using two monoclonal antibodies, was employed and the detection of the antibody–antigen interaction was performed through the analysis of an enzymatic reaction product by linear sweep voltammetry. Using the optimized experimental conditions the calibration curve (ip vs. log[HER2 ECD]) was established between 15 and 100 ng/mL and a limit of detection (LOD) of 4.4 ng/mL was achieved. These results indicate that the developed immunosensor could be a promising tool in breast cancer diagnostics, patient follow-up and monitoring of metastatic breast cancer since it allows quantification in a useful concentration range and has an LOD below the established cut-off value (15 ng/mL).

Imunossensores Eletroquímicos para o Diagnóstico Precoce e Descentralizado do Cancro da Mama

O cancro é uma das principais causas de morte em todo o mundo. Entre as mulheres, o cancro da mama é o mais frequente. A deteção precoce do cancro é de extrema importância na medida em que pode aumentar as possibilidades de cura dos pacientes e contribuir para a diminuição da taxa de mortalidade desta doença. Um método que tem contribuído para a deteção precoce do cancro é a análise de biomarcadores. Biomarcadores associados ao cancro da mama, como o Recetor 2 do Fator de Crescimento Epidérmico Humano (HER2) e o Antigénio Carbohidratado 15-3 (CA 15-3), podem ser detetados através de dispositivos como os biossensores. Neste trabalho foram desenvolvidos dois imunossensores eletroquímicos para a análise de HER2 e CA 15-3. Para ambos os sensores foram utilizados, como transdutores, elétrodos serigrafados de carbono. A superfície destes transdutores foi nanoestruturada com nanopartículas de ouro. Foram realizados imunoensaios não-competitivos (do tipo sandwich) em ambos os imunossensores, cuja estratégia consistiu na (i) imobilização do respetivo anticorpo de captura na superfície nanoestruturada dos elétrodos, (ii) bloqueio da superfície com caseína, (iii) incubação com uma mistura do analito (HER2 ou CA 15-3) e o respetivo anticorpo de deteção biotinilado, (iv) adição de estreptavidina conjugada com fosfatase alcalina (S-AP; a AP foi utilizada como marcador enzimático), (v) adição de uma mistura do substrato enzimático (3-indoxil fosfato) e nitrato de prata, e (vi) deteção do sinal analítico através da redissolução anódica, por voltametria de varrimento linear, da prata depositada enzimaticamente. Com as condições experimentais otimizadas, foi estabelecida a curva de calibração para a análise de HER2 em soro, entre 15 e 100 ng/mL, obtendo-se um limite de deteção de 4,4 ng/mL. Para o CA 15-3 a curva de calibração (em solução aquosa) foi estabelecida entre 15 e 250 U/mL, obtendo-se um limite de deteção de 37,5 U/mL. Tendo em conta o valor limite (cutoff value) estabelecido para o HER2 (15 ng/mL) pode-se comprovar a possível utilidade do imunossensor desenvolvido para o diagnóstico precoce e descentralizado do cancro da mama. No caso do CA 15-3 serão necessários estudos adicionais para se poder avaliar a utilidade do imunossensor para o diagnóstico do cancro da mama.