On the chaotic pole of attraction for Hindmarsh-Rose neuron dynamics with external current input

Cupolets in a chaotic neuron model

This paper reports the first finding of cupolets in a chaotic Hindmarsh-Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme by applying a binary control sequence. We demonstrate different neural dynamics (periodic or chaotic) of the Hindmarsh-Rose model through a bifurcation diagram where the external input current, I, is the bifurcation parameter. We select a region in the chaotic parameter space and provide the results of numerical simulations. In this chosen parameter space, a control scheme is applied when the trajectory intersects with either of the two control planes. The type of the control is determined by a bit in a binary control sequence. The control is either a small microcontrol (0) or a large macrocontrol (1) that adjusts the future dynamics of the trajectory by a perturbation determined by the coding function _r ( x ). We report the discovery of many cupolets with corresponding control sequences and comment on the differences with previously reported cupolets in the double scroll system. We provide some examples of the generated cupolets and conclude by discussing potential implications for biological neurons.

A Novel Evaluation Strategy to Artificial Neural Network Model Based on Bionics

With the continuous deepening of Artificial Neural Network (ANN) research, ANN model structure and function are improving towards diversification and intelligence. However, the model is more evaluated from the pros and cons of the problem-solving results and the lack of evaluation from the biomimetic aspect of imitating neural networks is not inclusive enough. Hence, a new ANN models evaluation strategy is proposed from the perspective of bionics in response to this problem in the paper. Firstly, four classical neural network models are illustrated: Back Propagation (BP) network, Deep Belief Network (DBN), LeNet5 network, and olfactory bionic model (KIII model), and the neuron transmission mode and equation, network structure, and weight updating principle of the models are analyzed qualitatively. The analysis results show that the KIII model comes closer to the actual biological nervous system compared with other models, and the LeNet5 network simulates the nervous system in depth. Secondly, evaluation indexes of ANN are constructed from the perspective of bionics in this paper: small-world, synchronous, and chaotic characteristics. Finally, the network model is quantitatively analyzed by evaluation indexes from the perspective of bionics. The experimental results show that the DBN network, LeNet5 network, and BP network have synchronous characteristics. And the DBN network and LeNet5 network have certain chaotic characteristics, but there is still a certain distance between the three classical neural networks and actual biological neural networks. The KIII model has certain small-world characteristics in structure, and its network also exhibits synchronization characteristics and chaotic characteristics. Compared with the DBN network, LeNet5 network, and the BP network, the KIII model is closer to the real biological neural network.

Optimal control and bifurcation diagram for a model nonlinear fractional SIRC

In this article, the optimal control for nonlinear SIRC model is studied in fractional order using the Caputo fractional derivative. Graph signal flow is given of the model and simulated by Simulink/Matlab which helps in discussing the topological structure of the model. Dynamics of the system versus certain parameters are studied via bifurcation diagrams, Lyapunov exponents and Poincare maps. The existence of a uniformly stable solution is proved after control. The obtained results display the activeness and suitability of the Mittag Generalized-Leffler function method (MGLFM). The approximate solution of the fractional order SIRC model using MGLFM is explained by giving the figures of solutions before and after control. Also, we plot the 3D relationships with different alpha (fractional order) which display the originality and suitability of the results.