This paper presents a novel chaotic four-wing attractor generated by coupling two identical Lorenz systems. An analysis of the proposed system shows that its equilibria have certain symmetries with respect to specific coordinate planes and the eigenvalues of the associated Jacobian matrices exhibit the property of similarity. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings of this new attractor are located around four equilibria with four unstable complex-conjugate eigenvalues. A generalization of the proposed system to realize an eight-wing attractor is also described.
This paper proposes a scheme for position estimation of randomly deployed sensor nodes in a wireless sensor network. Without GPS capability on any of the sensors, the position estimation is facilitated by beacons that move within the network. The beacons are equipped with GPS and can broadcast messages that contain the beacon identifiers and their current positions. With erroneous boundary beacon positions captured at the sensor, the sensor calculates its own position iteratively and updates the estimates upon newly acquired beacon positions. Practical implementation issues are discussed and simulation results show that the proposed iterative approach converges quickly even with beacon positions that have large errors.
Studying neurons from an energy efficiency perspective has produced results in the research literature. This paper presents a method that enables computation of low energy input current stimuli that are able to drive a reduced Hodgkin-Huxley neuron model to approximate a prescribed time-varying reference membrane voltage. An optimal control technique is used to discover an input current that optimally minimizes a user selected balance between the square of the input stimulus current (input current 'energy') and the difference between the reference voltage and the membrane voltage (tracking error) over a stimulation period. Selecting reference signals to be membrane voltages produced by the neuron model in response to common types of input currents i(t) enables a comparison between i(t) and the determined optimal current stimulus i*(t). The intent is not to modify neuron dynamics, but through comparison of i(t) and i*(t) provide insight into neuron dynamics. Simulation results for four different bifurcation types demonstrate that this method consistently finds lower energy stimulus currents i*(t) that are able to approximate membrane voltages as produced by higher energy input currents i(t) in this neuron model.
This paper describes the use of an interactive web-based circuit demonstration system to provide a mid-semester superposition capstone experience for electrical circuit fundamentals lab students. The particular circuit to be interactively demonstrated is a simple electronic artificial neural network which is used to compute individual and class average grades in our Electrical and Computer Engineering 100 Fundamentals of Circuits course. This provides a simple example of analog computing using a summing circuit. The analog grade computer is more fully described in a 1999 ASEE North Central Section Spring Conference paper by two of the authors of this paper entitled: "Neural Networks as a Source of Introductory Electrical Circuit Analysis Problems." The interactive system is based on a recently developed LabVIEW application for web-based circuit demonstrations which was subsequently enhanced to add distributed control of the circuit of interest. The resulting circuit demonstration emphasizes the key concepts of voltage division, superposition, circuit loading, and the principle of duality.
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