摘要:

The problem of simultaneously modeling the underlying nonlinear stochastic and deterministic dynamics of a time series is discussed. ©1996 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.51008

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A mathematical model of a neuron describing its oscillatory activity is constructed and investigated. The model in the form of a system of three ordinary differential equations demonstrates both regular behavior of the time dependence of electric membrane potential and its chaotic dynamics. The absence of rigorous heteroclinic trajectories in the phase space of the system is proved and the transition to chaos is investigated. The processes of synchronization of the oscillators are discussed. ©1996 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.51010

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

This work presents the most significant aspects of an original method of modelling and numerical simulation of nonlinear (linear) dynamical systems (1) it assures the local‐iterative linearization (LIL) of nonlinear (linear) differential equations and transforms them, in the close proximity of a pivot moment, into algebraic equations. The use of this method is illustrated in the study of a particular nonlinear dynamical systems. The conclusions highlight the advantages of the proposed procedure. ©1996 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.51011

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

What is a shell or a JIEKE (in Chinese) is introduced firstly, jieke is a sort of system boundary. From the concept of jieke theory, a new logistic model which takes account of the switch effect of the jieke is suggested. The model is analyzed and nonlinear mapping of the model is made. The results show the feature of the switch logistic model far differ from the original logistic model. ©1996 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.51012

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A review is given on the recent results in studying chaotic phenomena in weakly nonlinear systems. We are concerned with the class of chaotic states that can arise in physical systems with any degree of nonlinearity however small. The conditions for, and the mechanisms of, the transitions to chaos are discussed. These findings are illustrated by the results of the stability analysis of practical microwave and optical devices. ©1996 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.51013

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A technique for predicting chaos arising in a broad class of nonlinear oscillatory systems is proposed. It is based on the notion of running Lyapunov exponents and uses the local stability properties of trajectories for determining the ‘‘safe’’ areas in the phase space where any trajectory is regular and stable in the sense of Lyapunov. The combination of this approach with harmonic balance method permits to obtain the corresponding ‘‘safe’’ regions in the control parameter space. The borders of these regions may be considered as threshold lines delimiting the areas of possible chaotic instability. An example of the two‐well Duffing oscillator demonstrates good agreement between theoretically predicted values of control parameters where chaos arises with those obtained numerically. The technique is especially effective for rather high dissipation levels when other known methods such as Melnikov’s criterion or combination of harmonic balance with analysis of variational equations fail to provide correct results. ©1996 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.51014

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

In this paper, a new cryptosystem using dynamical systems is introduced which features storing information in stable configurations of dynamical systems but representing the information in arbitrary configurations of dynamical systems. The messagepin a plaintext can be considered as a stable configuration of a dynamical system. The encrypted string ofpin a ciphertext is an arbitrary configuration which will lead the dynamical system to the attractor defined by the original stringp. The encryption procedure,C=E(p), treats a string in a plaintext as an attractor of a finite dynamical system, and will generate a configurationCrandomly, as long as the configuration leads to a correct attractor. The decryption procedure regenerates attractors of a dynamical system,p=D(C)=D(E(p)), from the configurations contained in the ciphertext. Three families of cryptosystems (simple, compound, and stochastic cryptosystems) are presented. ©1996 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.51015

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A review of investigations of autosolitons in nonlinear systems which are of interest for the applied physics and for the transportation research is presented. Autosolitons are solitary intrinsic states which can be formed in a broad class of physical, chemical, biological dissipative distributed media and in traffic flow. Properties of autosolitons which are general for physical systems and for traffic flow will be discussed. Based on results of recent investigations of traffic jams in traffic flow, a comparison of nonlinear characteristics of traffic jams and with nonlinear properties of autosolitons which can be formed in active systems with diffusion will be given. Forms, properties, processes of evolution of autosolitons in traffic flow, in semiconductors and in gas discharge plasma are considered. ©1996 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.51016

出版商:AIP    

年代:1996

数据来源: AIP