Grid multi-wing butterfly chaotic attractors generated from a new 3-D quadratic autonomous system

Due to the dynamic characteristics of the Lorenz system, multi-wing chaotic systems are still confined in the positive half-space and fail to break the threshold limit. In this paper, a new approach for generating complex grid multi-wing attractors that can break the threshold limit via a novel nonlinear modulating function is proposed from the firstly proposed double-wing chaotic system. The proposed method is different from that of classical multi-scroll chaotic attractors generated by odd-symmetric multi-segment linear functions from Chua system. The new system is autonomous and can generate various grid multi-wing butterfly chaotic attractors without requiring any external forcing, it also can produce grid multi-wing both on the xz-plane and yz-plane. Basic properties of the new system such as dissipation property, equilibrium, stability, the Lyapunov exponent spectrum and bifurcation diagram are introduced by numerical simulation, theoretical analysis and circuit experiment, which confirm that the multi-wing attractors chaotic system has more rich and complicated chaotic dynamics. Finally, a novel module-based unified circuit is designed which provides some principles and guidelines for future circuitry design and engineering application. The circuit experimental results are consistent with the numerical simulation results.&nbsp

Adaptive Synchronization of Nonlinearly Parameterized Complex Dynamical Networks with Unknown Time-Varying Parameters

A new adaptive learning control approach is proposed for a class of nonlinearly parameterized complex dynamical networks with unknown time-varying parameters. By using the parameter separation and reparameterization technique, the adaptive learning laws of periodically time-varying and constant parameters and an adaptive control strategy are designed to ensure the asymptotic convergence of the synchronization error in the sense of square error norm. Then, a sufficient condition of the synchronization is given by constructing a composite energy function. Finally, an example of the complex network is used to verify the effectiveness of proposed approach

Evolution and maintenance of cooperation via inheritance of spatial neighbourhood

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Observer Design for a Core Circadian Rhythm Network

The paper investigates the observer design for a core circadian rhythm network in Drosophila and Neurospora. Based on the constructed highly nonlinear differential equation model and the recently proposed graphical approach, we design a rather simple observer for the circadian rhythm oscillator, which can well track the state of the original system for various input signals. Numerical simulations show the effectiveness of the designed observer. Potential applications of the related investigations include the real-world control and experimental design of the related biological networks

global relative parameter sensitivities of the feed-forward loops in genetic networks

It is well known that the feed-forward loops (FFLs) are typical network motifs in many real world biological networks. The structures, functions, as well as noise characteristics of FFLs have received increasing attention over the last decade. This paper aims to further investigate the global relative parameter sensitivities (GRPS) of FFLs in genetic networks modeled by Hill kinetics by introducing a simple novel approach. Our results indicate that: (i) for the coherent FFLs (CFFLs), the most abundant type 1 configuration (C1) is the most globally sensitive to system parameters, while for the incoherent FFLs (IFFLs), the most abundant type 1 configuration (I1) is the least globally sensitive to system parameters; (ii) the less noisy of a FFL configuration, the more globally sensitive of this circuit to its parameters; and (iii) the most abundant FFL configurations are often either the least sensitive (robust) to system parameters variation (IFFLs) or the least noisy (CFFLs). Therefore, the above results can well explain the reason why FFLs are network motifs and are selected by nature in evolution. Furthermore, the proposed GRPS approach sheds some light on the potential real world applications, such as the synthetic genetic circuits, predicting the effect of interventions in medicine and biotechnology, and so on. © 2011 Elsevier B.V.It is well known that the feed-forward loops (FFLs) are typical network motifs in many real world biological networks. The structures, functions, as well as noise characteristics of FFLs have received increasing attention over the last decade. This paper aims to further investigate the global relative parameter sensitivities (GRPS) of FFLs in genetic networks modeled by Hill kinetics by introducing a simple novel approach. Our results indicate that: (i) for the coherent FFLs (CFFLs), the most abundant type 1 configuration (C1) is the most globally sensitive to system parameters, while for the incoherent FFLs (IFFLs), the most abundant type 1 configuration (I1) is the least globally sensitive to system parameters; (ii) the less noisy of a FFL configuration, the more globally sensitive of this circuit to its parameters; and (iii) the most abundant FFL configurations are often either the least sensitive (robust) to system parameters variation (IFFLs) or the least noisy (CFFLs). Therefore, the above results can well explain the reason why FFLs are network motifs and are selected by nature in evolution. Furthermore, the proposed GRPS approach sheds some light on the potential real world applications, such as the synthetic genetic circuits, predicting the effect of interventions in medicine and biotechnology, and so on. © 2011 Elsevier B.V

Global relative parameter sensitivities of the feed-forward loops in genetic networks

It is well known that the feed-forward loops (FFLs) are typical network motifs in many real world biological networks. The structures, functions, as well as noise characteristics of FFLs have received increasing attention over the last decade. This paper aims to further investigate the global relative parameter sensitivities (GRPS) of FFLs in genetic networks modeled by Hill kinetics by introducing a simple novel approac