scholarly journals Simultaneity of Synchronization and Antisynchronization in a Class of Chaotic Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zhi Liu ◽  
Rongwei Guo ◽  
Yi Qi ◽  
Cuimei Jiang
Keyword(s):  
Numerical Simulations ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Synchronization Phenomenon ◽  
All Solutions ◽  
Necessary And Sufficient ◽  
Theoretical Results

In this paper, a new synchronization phenomenon, that is, the simultaneity of synchronization and antisynchronization, is investigated for a class of chaotic systems. First, for a given chaotic system, necessary and sufficient conditions for the simultaneity of synchronization and antisynchronization are proved. Then, based on these conditions, all solutions of such synchronization phenomenon for a given chaotic system are derived. After that, physical controllers that are not only simple but also implementable are designed to realize the simultaneity of synchronization and antisynchronization in the above system. Finally, illustrative examples based on numerical simulations are used to verify the validity and effectiveness of the above theoretical results.

ANALYTICAL CONDITIONS FOR AMPLITUDE DEATH INDUCED BY CONJUGATE VARIABLE COUPLINGS

2011 ◽  
Vol 21 (01) ◽  
pp. 225-235 ◽  
Author(s):  
XIAOMING ZHANG ◽  
YINGCHUN WU ◽  
JIANHUA PENG
Keyword(s):  
Numerical Simulations ◽  
Chaotic System ◽  
Arbitrary Number ◽  
Chaotic Systems ◽  
Amplitude Death ◽  
Chaotic Oscillators ◽  
Conjugate Variable ◽  
Global Coupling ◽  
Theoretical Results

We construct local and global conjugate variable coupled chaotic systems with an arbitrary number of identical chaotic oscillators. Amplitude death phenomena are found in these two kinds of systems. General methods are proposed to theoretically analyze conditions for amplitude death under local and global conditions, respectively. Taking the Rössler chaotic system as the oscillator unit, we apply these methods to determine the analytical conditions for amplitude death. And the transition relations between local and global coupling induced amplitude deaths are also given. All theoretical results are well confirmed by numerical simulations.

scholarly journals Necessary and Sufficient Conditions for Oscillation of Second-Order Delay Differential Equations

2020 ◽  
Vol 75 (1) ◽  
pp. 135-146
Author(s):  
Shyam Sundar Santra
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
All Solutions ◽  
Linear Delay ◽  
Delay Differential ◽  
Necessary And Sufficient

AbstractIn this work, we obtain necessary and sufficient conditions for the oscillation of all solutions of second-order half-linear delay differential equation of the form {\left( {r{{\left( {x'} \right)}^\gamma }} \right)^\prime }\left( t \right) + q\left( t \right){x^\alpha }\left( {\tau \left( t \right)} \right) = 0Under the assumption ∫∞(r(n))−1/γdη=∞, we consider the two cases when γ > α and γ < α. Further, some illustrative examples showing applicability of the new results are included, and state an open problem.

scholarly journals Oscillation Criteria of Solutions of Third Order Neutral Integro-Differential Equations

2021 ◽  
pp. 3642-3647
Author(s):  
Taghreed Hussein Abed ◽  
Sattar Naser Ketab ◽  
Hussain Ali Mohamad
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Third Order ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Necessary And Sufficient

      Some necessary and sufficient conditions are obtained that guarantee the oscillation of all solutions of two types of neutral integro-differential equations of third order. The integral is used in the sense of Riemann-Stieltjes. Some examples were included to illustrate the obtained results

12.—Rotation Properties of Adjoint Pairs of Differential Systems

1976 ◽  
Vol 75 (2) ◽  
pp. 149-155
Author(s):  
Kurt Kreith
Keyword(s):  
Differential Equations ◽  
Large Class ◽  
Fourth Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Differential Systems ◽  
All Solutions ◽  
Necessary And Sufficient

SYNOPSISA large class of self-adjoint fourth-order differential equations has the property that if one solution is oscillatory then all solutions are oscillatory. This paper establishes necessary and sufficient conditions for this property to hold for a corresponding class of non-self-adjoint differential equations.

scholarly journals Constructing complete chaotic maps with reciprocal structures

2005 ◽  
Vol 2005 (3) ◽  
pp. 357-372 ◽  
Author(s):  
Weihong Huang
Keyword(s):  
Numerical Simulations ◽  
Chaotic Maps ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Reciprocal Structures ◽  
Functional Forms ◽  
Necessary And Sufficient

A class of unimodal complete chaotic mapsf={fL,fR}with reciprocal functional forms(fR=1/fL)are examined. The necessary and sufficient conditions are provided to construct such maps. The theoretical conclusions are then verified by numerical simulations.

scholarly journals Lp,q-Label Coloring Problem with Application to Channel Allocation

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zhenbin Liu ◽  
Yuqiang Wu
Keyword(s):  
Wireless Network ◽  
Channel Allocation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Form ◽  
Logical Operators ◽  
Coloring Problem ◽  
All Solutions ◽  
Necessary And Sufficient

In this paper, the Lp,q-coloring problem of the graph is studied with application to channel allocation of the wireless network. First, by introducing two new logical operators, some necessary and sufficient conditions for solving the Lp,q-coloring problem are given. Moreover, it is noted that all solutions of the obtained logical equations are corresponding to each coloring scheme. Second, by using the semitensor product, the necessary and sufficient conditions are converted to an algebraic form. Based on this, all coloring schemes can be obtained through searching all column indices of the zero columns. Finally, the obtained result is applied to analyze channel allocation of the wireless network. Furthermore, an illustration example is given to show the effectiveness of the obtained results in this paper.

scholarly journals Collective Coordination of High-Order Dynamic Multiagent Systems Guided by Multiple Leaders

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Xin-Lei Feng ◽  
Ting-Zhu Huang ◽  
Jin-Liang Shao
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Second Order ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Multiple Leaders ◽  
Theoretical Results

For second-order and high-order dynamic multiagent systems with multiple leaders, the coordination schemes that all the follower agents flock to the polytope region formed by multiple leaders are considered. Necessary and sufficient conditions which the follower agents can enter the polytope region by the leaders are obtained. Finally, numerical examples are given to illustrate our theoretical results.

Exact regions of oscillation for a neutral differential equation

2000 ◽  
Vol 130 (2) ◽  
pp. 277-286
Author(s):  
S. S. Cheng ◽  
Y. Z. Lin
Keyword(s):  
Differential Equation ◽  
Sufficient Conditions ◽  
Neutral Differential Equation ◽  
Necessary And Sufficient Conditions ◽  
All Solutions ◽  
Constant Coefficients ◽  
Complete Set ◽  
Necessary And Sufficient

This paper is concerned with a neutral differential equation with four constant coefficients, one delay and one advancement. By means of the theory of envelopes, we consider all possible values of the parameters involved in the equation and obtain a complete set of necessary and sufficient conditions for all solutions to be oscillatory.

Chaotic Synchronization of a Controlled, Noised, Gyroscope System With an Expected Gyroscope System

2011 ◽  
Author(s):  
Fuhong Min ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Chaotic Synchronization ◽  
Necessary And Sufficient Conditions ◽  
Gyroscope System ◽  
Necessary And Sufficient

In this paper, chaotic synchronization of a controlled, noised gyroscope system with an expected gyroscope system is investigated. From the theory of discontinuous dynamical systems, the necessary and sufficient conditions of such synchronization are presented. Numerical simulations for non-synchronization, partial and full chaotic synchronizations of two gyroscope systems are carried out.

scholarly journals GENERALIZED SYNCHRONIZATION OF CHAOS VIA LINEAR TRANSFORMATIONS

1999 ◽  
Vol 09 (01) ◽  
pp. 215-219 ◽  
Author(s):  
TAO YANG ◽  
LEON O. CHUA
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Synchronization ◽  
Linear Transformations ◽  
Driving System ◽  
Driven System ◽  
Necessary And Sufficient ◽  
Special Case ◽  
Synchronization Manifold

Generalized synchronization (GS) of two chaotic systems is a generalization of identical synchronization. Usually, the manifold of GS is much more complex than the driven system and the driving system. In this paper, we study a special case of GS in which the synchronization manifold is linear (linear GS for short). In a theorem, we present the necessary and sufficient conditions under which a linear GS can be achieved between two chaotic systems. In particular, we study the linear GS of two Chua's circuits.

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