# Novel tracking function of moving target using chaotic dynamics in a recurrent neural network model

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Nara Shigetoshi, Jul 22, 2015 Available from:-
- "During this wandering, we have taken statistics of the residence time, the time during which the system continuously stays in a certain basin (Suemitsu and Nara 2004; Li and Nara 2008) and evaluated the distribution p(l, l) which is defined by pðl; lÞ ¼ fthe number of ljSðtÞ 2 b l in s t s þ l and Sðs À 1Þ 6 2 b l and Sðs þ l þ 1Þ 6 2 b l ; ljl 2 ½1; "

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**ABSTRACT:**Chaotic dynamics generated in a chaotic neural network model are applied to 2-dimensional (2-D) motion control. The change of position of a moving object in each control time step is determined by a motion function which is calculated from the firing activity of the chaotic neural network. Prototype attractors which correspond to simple motions of the object toward four directions in 2-D space are embedded in the neural network model by designing synaptic connection strengths. Chaotic dynamics introduced by changing system parameters sample intermediate points in the high-dimensional state space between the embedded attractors, resulting in motion in various directions. By means of adaptive switching of the system parameters between a chaotic regime and an attractor regime, the object is able to reach a target in a 2-D maze. In computer experiments, the success rate of this method over many trials not only shows better performance than that of stochastic random pattern generators but also shows that chaotic dynamics can be useful for realizing robust, adaptive and complex control function with simple rules.Cognitive Neurodynamics 12/2009; 4(1):69-80. DOI:10.1007/s11571-009-9101-5 · 1.77 Impact Factor -
- "Subsequently, chaotic artificial neural networks with the conventional sigmoidal activation functions were successfully implemented for solving various practical problems. Instances abound: chaotic simulated annealing was utilized to solve combinatorial optimization problems, such as the well-known traveling salesman problem [32]–[34]; chaotic itinerancy was applied to solve ill-posed problems, such as tracking a moving target [35], [36]. Moreover, it was found that the outputs of the chaotic neural network model with sigmoidal functions are always nonperiodic, changing continuously in a relatively narrow and asymmetric range, therefore, sometimes cannot be directly stabilized to one of its stored patterns or the corresponding reversed patterns. "

##### Article: Large memory capacity in chaotic artificial neural networks: a view of the anti-integrable limit.

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**ABSTRACT:**In the literature, it was reported that the chaotic artificial neural network model with sinusoidal activation functions possesses a large memory capacity as well as a remarkable ability of retrieving the stored patterns, better than the conventional chaotic model with only monotonic activation functions such as sigmoidal functions. This paper, from the viewpoint of the anti-integrable limit, elucidates the mechanism inducing the superiority of the model with periodic activation functions that includes sinusoidal functions. Particularly, by virtue of the anti-integrable limit technique, this paper shows that any finite-dimensional neural network model with periodic activation functions and properly selected parameters has much more abundant chaotic dynamics that truly determine the model's memory capacity and pattern-retrieval ability. To some extent, this paper mathematically and numerically demonstrates that an appropriate choice of the activation functions and control scheme can lead to a large memory capacity and better pattern-retrieval ability of the artificial neural network models.IEEE Transactions on Neural Networks 09/2009; 20(8):1340-51. DOI:10.1109/TNN.2009.2024148 · 2.95 Impact Factor -
- "Furthermore, the idea is extended to challenging application of chaotic dynamics in control. Chaotic dynamics introduced in a recurrent network model was applied to control tasks that an object should solve a two-dimensional maze for catching a target (Suemitsu and Nara 2004), or should capture a target moving along different trajectories (Li and Nara 2008). A simple coding method is employed to project the higher dimensional neural states dynamics into lower dimensional motion increments. "

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**ABSTRACT:**Originating from a viewpoint that complex/chaotic dynamics would play an important role in biological system including brains, chaotic dynamics introduced in a recurrent neural network was applied to control. The results of computer experiment was successfully implemented into a novel autonomous roving robot, which can only catch rough target information with uncertainty by a few sensors. It was employed to solve practical two-dimensional mazes using adaptive neural dynamics generated by the recurrent neural network in which four prototype simple motions are embedded. Adaptive switching of a system parameter in the neural network results in stationary motion or chaotic motion depending on dynamical situations. The results of hardware implementation and practical experiment using it show that, in given two-dimensional mazes, the robot can successfully avoid obstacles and reach the target. Therefore, we believe that chaotic dynamics has novel potential capability in controlling, and could be utilized to practical engineering application.Biological Cybernetics 10/2008; 99(3):185-96. DOI:10.1007/s00422-008-0249-6 · 1.93 Impact Factor