A universal unfolding of the Lorenz system is derived and studied in this paper. Both rigorous theoretical analysis and numerical simulations show that the Lorenz system, the Chen system, and the Lü system belong to the same universal unfolding. Therefore, they all have similar dynamical behaviors in the sense that if the Lorenz system has limit cycles produced from a Hopf bifurcation for a certain set of parameter values, then the other two systems also have limit cycles from the same set of parameter values; and if the Lorenz, Chen, and Lü systems are chaotic for some parameter values (for example, some typical parameter values), respectively, then the homotopic system for the Lorenz system and the Chen system, and the homotopic system for these three systems, are all chaotic within the entire domain of these homotopic parameters.
This brief describes methods based on time-delay feedback (TDF) for bifurcation control of nonlinear models of chaotic cardiac activity. We describe a nonlinear bifurcation controller that makes use of a feedback reference signal and a linear autoregressive formulation for the gain. This controller is effective at stabilizing two diverse cardiac maps to a variety of periodic orbits. We contrast our approach with the OGY method which has been used to control some chaotic biological processes and recently, some nonchaotic, stochastic ones.
No abstract is provided for this article.
This paper studies the security of a secure communication scheme based on two discrete-time intermittently chaotic systems synchronized via a common random driving signal. Some security defects of the scheme are revealed: 1) The key space can be remarkably reduced; 2) the decryption is insensitive to the mismatch of the secret key; 3) the key-generation process is insecure against known/chosen-plaintext attacks. The first two defects mean that the scheme is not secure enough against brute-force attacks, and the third one means that an attacker can easily break the cryptosystem by approximately estimating the secret key once he has a chance to access a fragment of the generated keystream. Yet it remains to be clarified if intermittent chaos could be used for designing secure chaotic cryptosystems.
The spreading (propagation) of diseases, viruses, and disasters such as power blackout through a huge-scale and complex network is one of the most concerned issues today. In this paper, we study the control of such spreading in a nonlinear spreading model of small-world networks. We found that the short-cut adding probability $p$ in the N-W model \cite{N-W:1999} of small-world networks determines the Hopf bifurcation and other bifurcating behaviors in the proposed model. We further show a control technique that stabilize a periodic spreading behavior onto a stable equilibrium over the proposed model of small-world networks.
This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter. Dynamical behaviors of the unified system are investigated in somewhat detail.
Evolutionary algorithms are cost-effective for solving real-world optimization problems, such as NP-hard and black-box problems. Before an evolutionary algorithm can be put into real-world applications, it is desirable that the algorithm was tested on a number of benchmark problems. On the other hand, performance measure on benchmarks can reflect if the benchmark suite is representative. In this paper, benchmarks are generated based on the performance comparison among a set of established algorithms. For each algorithm, its uniquely easy (or uniquely difficult) problem instances can be generated by an evolutionary algorithm. The unique difficulty nature of a problem instance to an algorithm is ensured by the Kruskal-Wallis H-test, assisted by a hierarchical fitness assignment method. Experimental results show that an algorithm performs the best (worst) consistently on its uniquely easy (difficult) problem. The testing results are repeatable. Some possible applications of this work include: 1) to compose an alternative benchmark suite; 2) to give a novel method for accessing novel algorithms; and 3) to generate a set of meaningful training and testing problems for evolutionary algorithm selectors and portfolios.
This paper studies robust impulsive synchronization of uncertain dynamical networks. By utilizing the concept of impulsive control and the stability results for impulsive systems, several criteria for robust local and robust global impulsive synchronization are established for complex dynamical networks, in which the network coupling functions are unknown but bounded. Three examples are also worked through for illustrating the main results.
No abstract is provided for this article.
No abstract is provided for this article.
Software-Defined Networking (SDN) benefits from the development flexibility of control-plane applications (SDN-Apps), which allows third parties to make contributions. Such flexibility may expose SDN networks to security threats, since SDN-Apps may be malicious or prone to implementation bugs. These buggy/malicious SDN-Apps may contaminate the data plane with abnormal network actions, which may not be prevented before they are committed to the data plane. This contamination may lead to network crash or poor network performance. We thus present ReSDN, a lightweight solution for data-plane state recovery, to recover an SDN data plane from a contaminated state. It requires neither switch modification nor the intervention of SDN-Apps, both of which current recovery solutions rely on. It leverages the concept of FP-tree (Frequent Pattern tree) to maintain the dependency of event transactions and network actions to achieve correct recovery. Our evaluations validate the viability of our ReSDN design, and show that it can recover more than twice as fast as the other type of recovery approach, rollback recovery.
A robust stabilization problem for general MIMO nonlinear systems is formulated in a Banach space setting in the time domain. Existence and uniqueness theorems are established, a general procedure for solving the problem is illustrated, and a simple example is included to show how the results can be applied.
