随机共振与非线性动力学行为的理论及神经放电中的机制

The stochastic resonance and the complicated behaviors of chaotic discharge of biologic neurons have become study forefront in nonlinear dynamics and broadly correlative subjects. There are many new phenomena and mechanics needing further search and study. And, in reality, these studies have many important requirements and applications. This project mainly worked on as follows: the relations between stochastic resonance and complicated behavior in nonlinear dynamics, the distinguishing between deterministic and stochastic mechanisms, the mechanism of stochastic resonance in ISI sequences of biologic neurons' firing and the control of stochastic resonance.. The main achievements are listed as follows: (1) The relations between stochastic resonance and the complexity, global characteristics in nonlinear dynamics are revealed. And the new mechanisms that stochastic resonance occurs in dynamic bistable systems and in neighborhood of bifurcation point for nonlinear systems with deterministic forcing and noise are obtained. The mechanisms that stochastic resonance occurs in inside wells and between wells in Duffing oscillator are revealed. The chaotic saddle and new crisis are found. (2) The control method on coherence resonance in excitable neurons, the control on fractal boundaries eroding safe basin and the control on magnetic levitation are provided. (3) The mechanism of spontaneous firing in neurons is revealed. And the distinguishing method on randomization and determination is given and has been applied on real neuron firing experiments. (4) The measurement quantities of stochastic resonance are developed. (5) The theoretical results on stochastic resonance in two-dimensional Brown movement and optical nonlinear systems are given out. (6) The correlative uncertainty in wada basin boundaries and riddled basins are studied. And the hyperchaotic attractor in Kawakami map is also given out.. The achievements have much scientific significance in finding new phenomena, new mechanisms, illuminating the relations of complicated behaviors and uncertainty of nonlinear dynamics with stochastic resonance, putting forward new theory and experimental methods and demonstrating the randomization and determination in biologic neurons firings. And the high-level comments of international authoritative referees for many papers of ours are given. The achievements of this project are a part of Nominating for National Science and Technology Prize of Ministry of Education. When the prize was applied, five academicians or professors appraised it as follows, " it is a high-level basal study and arrive at international advanced level wholly,….., and certain science influences have been brought out.".There are 6 papers published on international journals, 13 papers published on domestic journals, 6 papers read out in internal conferences, 5 papers submitted to journals; and there are 12 papers indexed by SCI and 3 dissertations are completed. And The Nominating for National Science and Technology Prize (Natural Science Prize) Second-Class Prize of Ministry of Education was awarded.

研究非线性动力学行为与随机共振的一些典型的、规律性的联系，某些复杂系统随机共振的理论及生物神经元簇放电随机共振机制，神经元信息传输和编码的确定性和随机性机制，随机共振的度量指标；随机共振的控制理论和实验；探讨生态、机电、能源等领域随机共振的例证。属于学科基础性问题又是学科前沿，有重要的理论意义和广泛的应用潜力。

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