WHEN CHRIS MINNIEAR, Cubmaster of Pack 998 in Mason, Ohio, was filling in as his son's Tiger Cub den leader, he tried a simple craft: making Kōnane (Hawaiian checkers) games. The cloth boards the boys made used flattened glass gems as game pieces. Things went well until near the end of the den meeting, when a pair of twins started throwing the glass gems. 'Getting that under control was fun,' he says.
- Gritli H and Belghith S (2015) Master-slave controlled synchronization to control chaos in an impact mechanical oscillator 2015 12th International Multi-Conference on Systems, Signals & Devices (SSD), 10.1109/SSD.20, 978-1-4799-1758-7, (1-6).
- Sonic games traditionally follow Sonic's efforts to stop Eggman, who schemes to obtain the Chaos Emeralds—seven emeralds with mystical powers. The Emeralds can turn thoughts into power, 195 warp time and space with a technique called Chaos Control, 196 197 give energy to living things, and be used to create nuclear or laser-based.
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- Continuous methods for chaos control were first proposed by Pyragas 3 and are based on continuous-time perturbations to perform chaos control. 6 proposed a control law named as the extended time-delayed feedback control (ETDF) considering the information of time-delayed states of the system represented by the following equations.
Fortunately, the incident happened at the end of the meeting. When he got home, Minniear realized the twins had managed to break every single game piece. Incidents like this taught Minniear how easily the controlled chaos of a den meeting can slip into uncontrolled anarchy.
How can you stop that from happening in your den? Here are some tips from Minniear and Caren Tamkin, a veteran San Diego Scouter who co-facilitated this summer's Strictly for Cub Scouters conference at the Philmont Training Center.
Know Your Boys
Step one, Tamkin says, is to know your Scouts. Learn what they like and what makes them lose control. When in doubt, ask a parent. Tamkin says she once had a boy in her den whom she suspected of having attention deficit hyperactivity disorder, although he hadn't been diagnosed. To get some insight into one boy's energetic personality, Tamkin asked the boy's mother to attend a few den meetings.
finance system 1.1. In this paper, we are interesting in delayed feedback control of the finance system 1.1.Theeffects of the time-delayed feedback on the finance system have long been investigated 5–8. Recently, different techniques and methods have been proposed to achieve chaos control.
Grandtotal 5 0 – create invoices and estimates. 'She observed what he was doing,' Tamkin says. 'She didn't discipline him or anything, but she did give me some tips to help me.' For example, the boy was able to concentrate much better when he was chewing gum or playing with a pencil, things Tamkin wouldn't have guessed without talking with the mother.
Establish Some Rules
Early in the Scouting year, establish some simple den rules (e.g., no hitting, no leaving the meeting room, no videogames). Put them on a poster that you display at every den meeting and refer to them often.
Many den leaders involve their Scouts in creating their own code of conduct, which works especially well with older boys. 'I found that the Wolves were so black and white in the way they viewed the world that they weren't really capable of coming up with a code of conduct that was loose enough for our purposes,' Tamkin says. 'When they got to Webelos, then they were really good at coming up with a den code of conduct.' Fasttasks 2 46 – the troubleshooting apple watch.
Be Flexible
Of course, rules are not enough to keep boys in line. You need a program that holds their interest and can require a good deal of flexibility.
'I am very big on improv,' Minniear says. To that end, he always has a backup plan he can quickly put into place.
At the same time, he will let activities run long if the boys remain interested. 'I'm not going to stop what's going on if they're getting some value out of it,' he says.
It also helps to remember that the real value of an activity may not be apparent on the surface. Once, Tamkin struggled to get her boys to make corsages for the pack's blue and gold banquet. Instead of the boys making them in one meeting, she had to space out the work over several meetings. 'It took us longer, and they weren't as perfect as I would have liked, but that wasn't the point,' she says. 'The point was for all the kids to work together.'
Reward Good Behavior
Tamkin recommends that dens use a marble jar to reward the group's good behavior. The concept is simple: Get a quart-size jar and a bag of marbles. At the end of each den meeting, have the boys rate how well they followed the den code of conduct. Put one or two marbles in the jar for each rule they obeyed. When the jar is full, treat the boys to ice-cream sundaes or playground time.
Tamkin says the key is to have the den rate its behavior as a group, not to point a finger at one misbehaving boy. Also, she says, 'I don't like the idea of taking something out of the jar [for bad behavior]. I don't want to get to the negative side.'
Some den leaders prefer to use a 'conduct candle' instead, blowing out the candle each time boys misbehave and offering a reward when the candle burns completely down. Tamkin prefers the marble jar because many meeting places ban open flames. Also, she says, 'When I did try the conduct candle, they wanted to see how long their hand could stay over the flame.'
Marble jars are safer, but be sure to keep the lid on your jar. After all, those marbles can be just as tempting as Kōnane game pieces.
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Chaos Control 1 6 2012 3rd Gen
Abstract
We investigate the local Hopf bifurcation in Genesio system with delayedfeedback control. We choose the delay as the parameter, and the occurrence of local Hopfbifurcations are verified. By using the normal form theory and the center manifold theorem,we obtain the explicit formulae for determining the stability and direction of bifurcatedperiodic solutions. Numerical simulations indicate that delayed feedback control plays aneffective role in control of chaos.
Control 1 Remote Codes
1. Introduction
Since the pioneering work of Lorenz [1], much attention has been paid to the study of chaos. Many famous chaotic systems, such as Chen system, Chua circuit, Rössler system, have been extensively studied over the past decades. It is well known that chaos in many cases produce bad effects and therefore, in recent years, controlling chaos is always a hot topic. There are many methods in controlling chaos, among which using time-delayed controlling forces serves as a good and simple one.
In order to gain further insights on the control of chaos via time-delayed feedback, in this paper, we aim to investigate the dynamical behaviors of Genesio system with time-delayed controlling forces. Genesio system, which was proposed by Genesio and Tesi [2], is described by the following simple three-dimensional autonomous system with only one quadratic nonlinear term: where , , < 0 are parameters. System (1.1) exhibits chaotic behavior when , , , as illustrated in Figure 1. In recent years, many researchers have studied this system from many different points of view; Park et al. [3–5] investigated synchronization of the Genesio chaotic system via backstepping approach, LMI optimization approach, and adaptive controller design. Wu et al. [6] investigated synchronization between Chen system and Genesio system. Chen and Han [7] investigated controlling and synchronization of Genesio chaotic system via nonlinear feedback control. Inspired by the control of chaos via time-delayed feedback force [8] and also following the idea of Pyragas [9], we consider the following Genesio system with delayed feedback control: where and .
2. Bifurcation Analysis of Genesio System with Delayed Feedback Force
It is easy to see that system (1.1) has two equilibria and , which are also the equilibria of system (1.2). The associated characteristic equation of system (1.2) at appears as As the analysis for is similar, we here only analyze the characteristic equation at . First, we introduce the following result due to Ruan and Wei [10].
Lemma 2.1. Consider the exponential polynomial where and are constants. As vary, the sum of the order of the zeros of on the open right half plane can change only if a zero appears on or crosses the imaginary axis.
Denote , , , , , , , , , . Following the detailed analysis in [8], we have the following results.
Lemma 2.2. (i) If , then all roots with positive real parts of (2.1) when has the same sum to those of (2.1) when .
(ii) If , , , then all roots with positive of (2.1) when has the same sum to those of (2.1) when .
Lemma 2.3. Suppose that , then , and .
Proof. Substituting into (2.1) and taking the derivative with respect to , we can easily calculate that thus the results hold.
Theorem 2.4. (i) If , then (2.1) has two roots with positive real parts for all .
(ii) If , , , then (2.1) has two roots with positive real parts for .
(iii) If , , and , then system (1.2) exhibits the Hopf bifurcation at the equilibrium for .
3. Some Properties of the Hopf Bifurcation
In this section, we apply the normal form method and the center manifold theorem developed by Hassard et al. in [11] to study some properties of bifurcated periodic solutions. Without loss of generality, let be the equilibrium point of system (1.2). For the sake of convenience, we rescale the time variable and let , , , , then system (1.2) can be replaced by the following system: where , and for , and are, respectively, given as By the Riesz representation theorem, there exists a function of bounded variation for , such that In fact, the above equation holds if we choose where is Durac function. For , let Then (1.2) can be rewritten in the following form: For , we consider the adjoint operator of defined by For and , we define the bilinear inner product form as
Suppose that is the eigenvectors of with respect to , then . By the definition of and (3.2), (3.4), and (3.5) we have Hence Similarly, let be the eigenvector of with respect to , by the definition of and (3.2), (3.4), and (3.5) we can obtain Furthermore, , .
Let , where is the solution of (3.7) when . We denote , then We Rewrite (3.13) in the following form: where Noticing that we have Define with On the other hand, Expanding the above series and comparing the corresponding coefficients, we obtain While Let , then we have Therefore we have Comparing the corresponding coefficients, we have
In what follows we will need to compute and . Firstly we compute , when . It follows from (3.18) that Substituting the above equation into (3.21) and comparing the corresponding coefficients yields By (3.21), (3.28), and the definition of we have Hence Similarly we have
In what follows, we will seek appropriate and in (3.30) and (3.31). When , with Comparing the coefficients in (3.18) we have By (3.21) and the definition of we have Substituting (3.30) into (3.36) and noticing that we have namely, Thus where Following the similar analysis, we also have hence where Thus the following values can be computed:
It is well known in [11] that determines the directions of the Hopf bifurcation: if , then the Hopf bifurcation is supercritical(subcritical) and the bifurcated periodic solution exists if ; determines the period of the bifurcated periodic solution: if , then the period increase(decrease); determines the stability of the Hopf bifurcation: if , then the bifurcated periodic solution is stable(unstable).
4. Numerical Simulations
In this section, we apply the analysis results in the previous sections to Genesio chaotic system with the aim to realize the control of chaos. We consider the following system: Obviously, system (4.1) has two equilibria and . In what follows we analyze the case of only, the analysis for is similar. The corresponding characteristic equation of system (4.1) at appears as Hence we have , , , , , , , , , . By Theorem 2.4, when , that is, , (4.2) has two roots with positive real parts for all . In order to realize the control of chaos, we will consider . We take as a special case. In this case, system (4.1) takes the form of Thus we can compute , , , , , , , , , , ,. Therefore, using the results in the previous sections, we have the following conclusions: when the delay , the attractor still exists, see Figure 2; when the delay , Hopf bifurcation occurs, see Figure 3. Moreover, , , the bifurcating periodic solutions are orbitally asymptotically stable; when the delay , the steady state is locally stable, see Figure 4; when the delay , the steady state is unstable, see Figure 5. Numerical results indicate that as the delay sets in an interval, the chaotic behaviors really disappear. Therefore the parameter works well in control of chaos.
Control 1 Remote
5. Concluding Remarks
In this paper we have introduced time-delayed feedback as a simple and powerful controlling force to realize control of chaos of Genesio system. Regarding the delay as the parameter, we have investigated the dynamics of Genesio system with delayed feedback. To show the effectiveness of the theoretical analysis, numerical simulations have been presented. Numerical results indicate that the delay works well in control of chaos.
Acknowledgment
This work was supported by the Research Foundation of Hangzhou Dianzi University (KYS075609067).
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Copyright
Copyright © 2012 Junbiao Guan. This is an open access article distributed under theCreative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
